Glasgow City Council said the cash would be spent on more segregated cycling routes, traffic calming measures and other safety features.
Councillors approved the Strategic Plan for Cycling 2016-2025 and agreed to the funding on the basis that match funding is sourced from other key stakeholders.
The number of people cycling in Glasgow has increased by 200% since 2007.
Since 2010, the cycle network in the city has grown from 230km to 310km.
Facilities such as the Sir Chris Hoy Velodrome, at Emirates Arena, and Cathkin Braes Mountain Bike Trails have also opened during that time.
Bailie Elaine McDougall, the council's executive member for transport, environment and sustainability, said: "Cycling has huge health benefits for individuals as well as environmental advantages for the city.
"This new strategy outlines our plans to transform Glasgow into the most cycle friendly city in Scotland.
"To achieve this will require substantial investment and it is our intention to invest £6m over the next three years if we can get the Scottish government and other stakeholders to do the same."
Scotland's largest council aims to spend £6m over the next three years on improving cycling infrastructure.