The channel, which is publicly owned but commercially funded, will not sell its London headquarters but plans to establish a new base where “creative decision makers who are spending money” will be located, chief executive Alex Mahon said.
The move will be part of the biggest restructure of Channel 4 in its 35-year history with two new smaller hubs outside London also to be established in 2019.
A bid process across the UK opens this month with a decision to be made later in 2018.
Mr Cosgrove, who served as Channel 4 Controller of Arts and Entertainment and then Head of Programmes (Nations and Regions) until 2015, will chair a new board created to guide Glasgow’s pitch.
Led by Glasgow City Council, with support from the Scottish Government, the board will also include representation from the city’s creative industries.
Mr Cosgrove said: “Glasgow has everything Channel 4 needs in a new home - including a dynamic and original independent broadcast sector.
“The same values and qualities that typify Glasgow are ingrained in the culture and identity of Channel 4. They are bold and provocative, with real heart - and they both attract and celebrate innovative and diverse people.
“Channel 4 and Glasgow are made for one another.”
The channel currently has more than 800 staff but fewer than 30 based outside central London.
Some 300 jobs will now be moved to the new locations, with the intention to grow further over time.
Glasgow City Council leader Susan Aitken said: “I’m delighted Stuart has agreed to chair Glasgow’s bid.
“Both this city and the channel are clearly close to his heart - and there is nobody who better understands how the two can complement each other.”
Glasgow’s bid has received support from established broadcasters in Scotland.
Mark Hedgecoe, head of BBC Studios, Pacific Quay Productions, said: “We are very excited about Glasgow’s bid.
“BBC Studios has a range of production bases around the UK and has a commitment to making programmes outside London.
“Given Pacific Quay Productions are based in Glasgow, we are well aware of the huge attractions and advantages of making programmes in the city. We fully back the bid.”