Leeds City Council has now approved the scheme which is part of the £270m Connecting Leeds programme.
Sisk will start in June to transform Call Lane, New Market Street, Kirkgate, Lower Briggate Duncan Street and parts of Vicar Lane and Boar Lane.
Work will include widening pavements, introducing more greenery and improved public realm.
The scheme will also offer priority for pedestrians and cyclists in a bid to encourage a modal shift from private cars to walking, cycling and public transport use.
The expected completion date for all of the work is by winter 2021.
Leeds City Council’s executive member for climate change, transport and sustainable development, Councillor Lisa Mulherin, said: “The enhancements will place the iconic buildings of the Corn Exchange and Kirkgate Market in a more appropriate setting.
“The bus priority measures and improved walking and cycling routes will improve connectivity services and air quality in the city.
“Like all major schemes, there will be disruption, however Leeds City Council will work closely with the bus companies, other transport providers and business to keep this to a minimum and will work hard to keep the public informed of changes which affect them.”