The new Bedfordshire, Hertfordshire and Buckinghamshire service was switched on at 08:46 GMT at Bletchley Park.
At Bletchley Park, the original Colossus cracked messages sent by Hitler's generals during World War II.
BBC: Tony Sale: Computer restoration memorial prize launched
Players can move their pieces from his birthplace in Maida Vale to Hut 8 at Bletchley Park.
The rebuild of Edsac will be done in public at the National Museum of Computing at Bletchley Park.
BBC: Work begins on hardware to aid Edsac replica recreation
Funds raised by the sale of the game at Bletchley Park will aid the heritage site's reconstruction project.
One of the first huts to house the Enigma code breaking device at Bletchley Park is to be restored.
Search giant Google has bought 1, 000 of the sets and donated them to Bletchley Park to help raise funds.
Mr Hague also used his visit to announce a boost in funding for the preservation of Bletchley Park, the forerunner to GCHQ.
BBC: Cybercrime-fighters seek 'generation Xbox' for spy jobs
The hand-drawn version was thought to have been lost but was rediscovered in 2011 and donated to the Bletchley Park museum soon after.
He has performed at Bletchley Park and will return there this month to the National Computer Museum to play live with Orchestral Manoeuvres in the Dark.
Tony Sale was the brilliant engineer who rebuilt the Colossus computer, established The National Museum of Computing at Bletchley Park and founded the Computer Conservation Society.
Bletchley Park was the wartime home of the Government Code and Cypher School which broke the codes generated by the German Enigma machine, using the Bombe.
Based at Bletchley Park, the mathematician was part of the team that cracked the Nazi Enigma code - a vital part of the allied war effort.
Capt Roberts, from Liphook, has been working for recognition for Bletchley Park's "4T's" - the Testery as a whole, and three colleagues responsible for major discoveries.
Ahead of the launch workers at Bletchley Park - the site of Britain's World War II codebreaking efforts - trialled the software to help promote the roll-out.
While the grand, though not beautiful, main house is the most iconic image of Bletchley Park, the huts were where much of the real work took place.
BBC: Bletchley Park enigma code huts prepare for restoration
Iain Standen from the Bletchley Park Trust said the exhibition gave "long-awaited recognition to the short but brilliant life and legacy of Alan Turing, the father of computing".
"Bringing this board to life has been one of the most exciting and unique projects we've been involved with here, " said Iain Standen, head of the Bletchley Park Trust.
The National Museum of Computing (TNMOC) at Bletchley Park, Buckinghamshire, has been at the centre of efforts to fill the gap and ensure the full story of wartime computer development is told.
Foreign Secretary William Hague MP launched the competition at codebreaking museum Bletchley Park in October 2012, as part of three GCHQ initiatives aimed at attracting young people into maths and computer science.
He was the driving force behind the rebuild of the famous Colossus computer and one of the founders of The National Museum of Computing at Bletchley Park, as well as being a British spy-catcher.
The special board has Bletchley Park, the wartime centre of the Allied code-cracking effort, taking the place of Mayfair, swaps houses and hotels for huts and blocks and has Turing's face on all the banknotes.
Mr Turing worked as part of the team which cracked the Enigma code at Bletchley Park in World War II and went on to help create the world's first modern computer, the Manchester Small-Scale Experimental Machine.
Prior to embarking on the Colossus rebuild, Mr Sale worked at the Science Museum and, with Doron Swade, drove the recreation of other pioneering computers and helped found the CCS. He was also involved in the campaign to save Bletchley Park and was one of the founders of the National Museum of Computing.
BBC: Tony Sale: Computer restoration memorial prize launched
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