The design and build contract was first valued at around £31m two years ago but has now risen to an expected £35m.
A selected contractor will deliver a 1.7km long single carriageway road that includes a 500m long viaduct crossing of the river Great Ouse and a separate bridge over a railway line.
The new route leaves the A142 Stuntney Causeway to the south-east of Ely, before re-joining the existing A142 at a new roundabout on Angel Drove.
The two-year contract is hoped to start in early August. Information about prequalification to bid can be obtained from the website.