The Departments of Transport and for Communities and Local Government have both passed the plan, subject to developers contributing £45 million and Central Bedfordshire Council £5 million.
Both are on track to happen and work is due to start on the road in 2014.
Mr Selous, who has campaigned for the link since he was elected to Parliament in 2001, said: “This is wonderful news for the whole of South West Bedfordshire."
Traffic jams in Dunstable and Houghton Regis will be reduced and villages such Totternhoe, Kensworth and Toddington will see much less through traffic, he added.
Leighton Buzzard and Linslade will get fast direct access to the M1 and the whole motorway network, which will help business growth in the town. Aylesbury will also reap the benefit, the MP said.
Mr Selous paid tribute to the work of Central Bedfordshire Council in securing the developer contribution.
He added: “I believe that South West Bedfordshire will now realise its full potential in creating jobs and wealth.”