The company bought the substantial plot 12 years ago but since then it has been lying derelict.
It has now sold it to a joint venture which plans to build high quality flats and shops.
Candleriggs is a 50/50 project between the investment arm of Mace and funds managed by Mercer Real Estate Partners.
The partnership intends to submit a planning application for the site by the end of this year and will talk to people and businesses to find our their views.
Mike Miles, development director of Mace, said: "We are incredibly excited to have acquired the site and we look forward to developing proposals in conjunction with Glasgow City Council and local stakeholders.
"We are fully committed to developing a high class scheme that will positively contribute to the Merchant City."
David Grover, chief operating officer of investment for Mace, said: "Glasgow is undergoing a huge transformation at the moment and we are delighted to be working on such a great project.
"The investment compliments our wider portfolio of projects around the UK focused on mixed use urban regeneration and we will be bringing our expertise to this development."
In the past, Selfridges blamed the world-wide economic downturn for the decision not to press ahead with a store in the Merchant City.
A spokesman for the upmarket company said: "The decision was taken to find an appropriate buyer with an exciting and cohesive vision for the redevelopment of such a large site.
"We are confident we have selected the right purchaser and look forward to seeing the proposals developed by the Candleriggs team."
City council leader Gordon Matheson, who represents the Merchant City area, welcomed the decision to sell the site.
He said: "It's great news plans for the redevelopment of the Candleriggs site are now progressing.
"Local residents and businesses are delighted the site has been cleared over recent weeks and are looking forward to seeing it brought back to life.
"The plans for the Candleriggs site will, I am sure, be of the very highest quality and very exciting.
"The council and the local community will look forward to working with Mace and Mercer Real Estate Partners on their plans, which when complete will strengthen Merchant City's position as a jewel in Glasgow's crown."
Glasgow Chamber of Commerce chief executive Stuart Patrick said: "Over a decade has passed since Selfridges bought this site and the Merchant City could ill afford to have such a substantial and important parcel of land unused and unproductive.
"It is good news for Glasgow city centre that the development plans will bring more people to live there and contribute to the vibrancy and economy of the area - as well as add to its retail offering."