The viaduct is 120 years old, and the council has also set aside a further £450,000 to assist with the project.
Route 23 is part of the National Cycle Network, and currently there are two sections between the Southampton to Basingstoke link that are missing. The first part will be completed later this summer, running through Winnall, and the second will run along the site of the Hockley Viaduct at the southern end of the city.
Hampshire County Council and the cycling charity Sustrans will be joining the city council working on the project, which local MP Steve Brine has welcomed.
He said: "I very much welcome this news, having spent some time with campaigners recently. The viaduct really is a wonderful part of our heritage, and I am delighted that the city council is onside with local cyclists (including myself) on this one."
Council leader Cllr George Beckett added: "This project has great potential to connect the cycle routes across Winchester and to ensure a local landmark is preserved for the future.
"We have been working hard for some time to find a way forward, and we are pleased to be able to start the exploratory work needed to try to make this project a reality with the support from other key partners."
Pictured; Steve visited the Hockley Viaduct site earlier this year