Thordarson, 53, replaces Steve Holland who was relieved of his duties at the Alexandra Stadium in November. He will take charge of the Alex for the first time in the FA Cup third round tie against Millwall at the New Den on 3 January.
Thordarson told BBC Radio Stoke: "It will be a big challenge, but I'm looking forward to it. I know it will require a lot of hard work and commitment. It won't be easy, but I'm ready to take it on. The challenge is one of the things that attracted me to the job. A job without a challenge is hard to get motivated for. I want to build a team, to make things happen rather than wait for them to happen."
The Icelander became Stoke City's first non-British manager in 1999, leading the Potters to the Football League Trophy in 2000. He then led the Potters to promotion via the play-offs in 2002, but left the club in the same summer after his contract was not renewed. Thordarson then went on to have spells in charge of Barnsley and Notts County before returning to his homeland to manage Akranes in 2006.
Current caretaker manager Dario Gradi will continue to look after first-team affairs for the League One fixtures against Oldham and Hartlepool on Boxing Day and 28 December respectively. He will then return to his previous role as technical director.
Another club who have filled the managerial slot is Swindon Town who have appointed Danny Wilson as their new manager.
The former Northern Ireland international's first game in charge will be Sunday's visit of Brighton. Wilson, 48, was out of work for less than two weeks following his sacking as Hartlepool manager earlier this month after two-and-a-half years in charge.
Leeds United 1 Leicester City 1
New Leeds boss Simon Grayson has his work cut out to revive the fortunes at Elland Road despite watching his side claim a late point against leaders Leicester.
Leeds may have a new manager but the same problems continue to plague their defence and Matt Oakley quickly fired Leicester ahead with a 25-yard effort in the 24th minute.
Leicester have been in impressive form all season but failed to find the killer blow with Matty Fryatt wasting a golden opportunity after the restart.
Leeds persevered throughout and with a little bit of luck pulled level in the dying seconds when Robert Snodgrasss lashed home Luciano Becchio's pin-point cross.
Bristol Rovers 1 MK Dons 2
Bristol Rovers defender Byron Anthony had a day to forget as ten man MK Dons kept up the pressure on league leaders Leicester at The Memorial Stadium.
Roberto Di Matteo's troops flew out of the blocks and found themselves a goal ahead through Aaron Wilbraham in the 14th minute but a man down minutes later when Miguel Angel Llera picked up a second yellow.
However the lead lasted less than 60 seconds and Jo Kuffour pulled The Gas level after a well-worked move straight from the kick-off caught The Dons cold.
But just as the hosts pressed for a second their worst nightmare struck when Anthony spooned a routine cross into his own net in the 59th minute.
Peterborough United 1 Millwall 0
Aaron Mclean grabbed the only goal as Peterborough edged past the 10 men of fellow promotion-hopefuls Millwall.
Mclean found the net with a well-placed 23rd-minute shot after being sent clear by strike partner Craig Mackail-Smith.
But Posh could not turn their numerical advantage into more goals despite Millwall having defender Tony Craig dismissed for elbowing Chris Whelpdale.
Mackail-Smith saw an effort ruled out for offside and shot wide while Gary Alexander headed wide for the Lions.
Scunthorpe United 3 Hartlepool United 0
Scunthorpe duo Grant McCann and Gary Hooper both found the net as The Iron began to plot a New Year revival during an easy win over Hartlepool.
Scunthorpe raced into the lead in the first-half thanks to McCann's thumping 25-yard free-kick in the 32nd minute.
The Iron picked up where they left off after the restart and Hooper all but sealed the win with his 16th goal of the season in the 47th minute.
And Paul Hayes made sure there was no way back for Hartlepool from the spot late on after Sam Collins hauled down former Millwall striker Ben May.
Crewe Alexandra 0 Oldham Athletic 3
Controversial striker Lee Hughes' second-half double gifted Oldham all three points as The Latics ran riot to see off rock bottom Crewe.
Hughes should have opened his account in the first-half but somehow failed to hit the target after finding himself clean through.
However it made no difference after the break when former Millwall striker Darren Byfield netted his first goal for nearly a year in the 57th minute.
Hughes banished his first-half woe completing a swift three-man move 11 minutes later before netting his second with a smart header five minutes from time.
Walsall 1 Stockport County 0
Ten-man Walsall held off a late Stockport onslaught to record their first win in four thanks to defender Rhys Weston.
After a dire first-half at The Bescot Stadium - Weston dealt Stockport a killer blow in the 64th minute heading home Chris Palmer's corner.
However The Saddlers had hearts in their mouths in the last 25 minutes when Michael Ricketts picked up his second yellow after hauling down Gary Dicker moments later.
Hereford United 2 Tranmere Rovers 2
Hereford striker Stephen Guinan netted his sixth goal of the season as The Bulls twice came from behind to claim a vital point against Tranmere.
Ronnie Moore's Rovers thought they had done enough to go into the break ahead when Edrissa Sonko fired them in front in the 37th minute.
But it wasn't to be and the struggling Bulls were given a lifeline when Toumani Diagouraga latched onto Lionel Ainsworth's through ball and fired home in the 45th minute.
It was the same story in the second half with Sonko adding his second in the 61st minute only for Guinan to pounce and claim a point four minutes later.
Carlisle United 3 Huddersfield Town 0
Carlisle duo Danny Graham and Michael Bridges both netted as The Cumbrians sent Huddersfield and new manager Lee Clark back to the drawing board at Brunton Park.
Carlisle's last win came over Grays last month in the FA Cup but they took a shock lead when Graham pounced and fired home his 13th of the season in the 12th minute.
The Cumbrians flew out of the blocks after the restart and Bridges was on hand to add the killer touch and only his second of the season in the 55th minute following a following move from defence.
Huddersfield were reeling by now and Sunderland loanee Graham Kavanagh made matters worse completing the rout in the 75th minute.
Southend United 1 Northampton Town 0
The clash at Roots Hall came to life as late as the 75th minute when Abdul Osman was given his marching orders after a late foul on Johnny Herd.
Southend immediately pressed for the winner and it finally came with the last kick of game - West Ham winger Stanilas curling a free-kick past the outstretched hand of Cobblers keeper Chris Dunn.
For a full report and player markings go here: www.thelittlegazette.com/news/loadnews.asp?cid=TMNW&id=423974
Brighton 1 Colchester 2
Colchester striker Scott Vernon netted a last-gaps winner as the pressure begins to mount on struggling Brighton boss Micky Adams.
Brighton have recorded only one point from their last six games but were celebrating in the 21st minute when Nicky Forster lashed home his first goal in seven games.
However the lead didn't last long and Colchester struck back in fortunate fashion when Adam Hinshelwood spooned into his own net minutes later.
The Seagulls never recovered after the break and Colchester's patience paid off in the 87th minute when Vernon latched onto Kemal Izzet's through ball and fired home.
Leyton Orient 1 Swindon Town 2
Swindon gave new boss Danny Wilson something to smile about in the stands at Leyton Orient thanks to Jack Smith's second-half penalty.
The Robins got off to the perfect start when Lee Peacock danced his way into the box and lashed home as early as the first minute.
Swindon were back at it after the restart when Jack Smith slotted home from the spot after Alton Thelwell handled inside the area.
But just as the visitors sat back former West Brom defender Tamika Mkandawire netted with 11 minutes to go to set up a tense finish.
Yeovil Town 1 Cheltenham Town 1
On loan striker Luke Rodgers issued a come and get me plea to Yeovil boss Russell Slade after single-handedly salvaging a point against Cheltenham.
Cheltenham weathered a first-half Glovers storm and went in at the break a goal ahead when Ashley Vincent netted his fourth of the season.
The Robins haven't kept a clean sheet away from home in their last 20 games and it wasn't about to change against Yeovil.
Rodgers - on-loan from Port Vale and hopeful of a permanent move to The Glovers next month - pounced in the 75th minute heading home Andrew Welsh's cross.
Coca-Cola Football League One
|Latest match Friday,|
26th December 2008
|2||Milton Keynes Dons||22||7||0||4||20||11||8||1||2||26||12||15||1||6||46||23||46||+23|
|21||Brighton & Hove Albion||22||2||4||5||15||19||2||4||5||10||15||4||8||10||25||34||20||-9|