This new route will see two new stations built, one at Tempsford or St Neots and one for Cambourne.
This will lead to the government making a final decision on whether to take this project forward, and to make an application for a developed consent order.
Supporters are now hoping for a statement in the next Budget, although the project could be set back by spending commitments to HS2 and Northern Power Rail.
The line will be the final stage of the Oxford-Cambridge Arc, and would support opportunities for house building growth.
Construction in the second part of the project, between Bicester and Bedford, is already underway and should be completed by 2023. The new line should be completed by 2030.
Backers of the project East West Rail consortium chair Mark Shaw said: “The Central Section between Bedford and Cambridge has always been the most challenging part of planning East West Rail, given that – unlike the section west of Bedford – it requires a completely new route.
“This announcement ensures the momentum established by the East West Railway Company is maintained and we will continue to work closely with them as they look to secure detailed planning consent and get trains on tracks at the earliest opportunity.”
Housing Secretary Robert Jenrick said: “The announcement is great news for the region.
“These plans could see significant improvements to transport links across the Oxford-Cambridge Arc, one of the most exciting economic growth opportunities in Europe, while also potentially helping us to deliver the homes that people need.”