The council argued the roundabout at junction 10a was the weak link between £800m improvements to the M1 and the recently completed East Luton Corridor.
The funding agreement will allow the town to press ahead with its plan to remodel the roundabout, which has been on the cards for six years.
Now an application will be submitted to the Infrastructure Planning Commission at the end of this year, with a public hearing in spring 2012.
The project would see the removal of the existing roundabout and widening of the M1 spur road to three lanes, to provide a continuous east-west carriageway with a speed limit of 50mph.
Two new roundabouts would be built to allow road users to join and leave London Road and the M1 spur. London Road itself would be realigned, to pass under the M1 spur, with pedestrians and cycle routes also provided.
The council needs to stump up £6.5m of its own cash for the scheme, and says it has already managed to secure £3m from private developers.
Congestion at the junction has been holding up final planning approval for the West Ferry Printers move from London to the former DHL base in Kimpton Road, Luton.
Transport minister Theresa Villiers said: “I expect this scheme will create a huge number of jobs – potentially up to 2,000 – in construction and from employment at surrounding sites, plus it will really unlock the full benefits of previous improvements to the M1 and Airport Way.
“By improving J10a of the M1, the south and east of Luton will receive a major boost for local employment and housing.
Drivers will also get a welcome relief from the traffic jams that are such a headache on this part of our road network.”