The new road bridge will give access to the Middlehaven Dock regeneration site and pave the way for further development on the 100ha site.
It will replace a footbridge that was installed following the removal an earlier swing bridge by the Teesside Development Corporation.
Construction is expected to start in spring 2015 and will take a year to complete.
The bridge and associated improvements will complete the road network serving the north of the town, connecting Greater Middlehaven and Riverside Park with an east-west spine road running parallel to the A66 and linking directly to it at either end.
The development will also create further opportunities for the regeneration of the Dock as a marina and centre for water sports and general recreational and leisure use, the council said.