The contractor will start next month on finalising the design of the crossing, ready for building.
The award of the construction stage of the contract, is scheduled to be announced in the Autumn of 2019.
Councillor Matthew Hicks, leader of Suffolk County Council, said: “Following diligent work from the project teams at the council, we have selected a contractor which we believe brings a balance of high-quality work and value for money.
“BAM Nuttall already has strong links to the region, having worked on projects such as Great Yarmouth Flood Alleviation Scheme and ABP Ipswich Quay Works.
“They also have a regional base in Thetford and earlier this year, held an event to meet contractors in the area to help support the local economy.”
Ewan Barr, Project Director at BAM Nuttall said: “We’re excited to be involved in a project which is going to have such a positive impact on people and businesses in Lowestoft.
“We have an award-winning track record of working on projects of national importance and look forward to delivering a new iconic landmark for the town and the east of England.
“We plan to open an office near the construction site in the coming months.”