The city council is to borrow £20.5m to fund the majority of the project, which aims to extend the lifespan of the National Cycling Centre by 25 years.
“The National Cycling Centre is an incredible asset for this city,” said Cllr Rabnawaz Akbar, executive member for neighbourhoods at Manchester City Council.
“Failure to act now would risk undermining of Manchester’s reputation as a sporting capital.”
Investing now will avoid future building failures and unexpected closures or services having to be withdrawn, and save money in the longer term, the council said.
Work to refurbish the 130,000 sq ft building will begin after the rescheduled Tokyo Olympics and will focus on making the venue more energy efficient.
The £26m scheme includes work to refurbish changing rooms, and the installation of air-source heat pumps to replace the gas boilers.
The velodrome’s energy systems, lighting, roof, water supply, scoreboard and timing systems will all be upgraded in line with the council’s 2038 zero-carbon deadline.
Ellis Williams Architects is leading on the design of the project and ISG has been appointed as the main contractor.
Brian Facer, chief executive of British Cycling, said: “Without the National Cycling Centre, we would not have been able to produce riders of the calibre of Sir Chris Hoy and Dame Sarah Storey.
“This investment will mean Manchester can continue to lead the way for the rest of the country by providing a vital facility where some of the world’s greatest riders can be supported by a fantastic team to achieve their best.”