The agreement, under the council's Glasgow Guarantee jobs scheme, will see the posts going to long term unemployed and ex-servicemen and women via the council's Helping Heroes project.
Gordon Matheson, leader of Glasgow City Council, is announcing the deal today at the Scottish Labour Party conference in Perth.
First Glasgow has also agreed to create an extra 150 jobs each year to help even more people back into work.
Mr Matheson said: "First Glasgow's commitment to the programme is fantastic news and shows a real understanding of just how important the Glasgow Guarantee is to our city.
"I am delighted that this partnership will specifically target our armed forces veterans. If you have fought for your country you shouldn't have to fight for a job when your service ends.
"These new jobs will make a real difference to the men and women who have served our country so well, often in challenging and harrowing environments and First Glasgow are to be commended for their commitment."
Mr Matheson previously said the £50 million Glasgow Guarantee programme, which helps unemployed people back into work and young people and care levers get apprenticeships, will continue until 2018.
So far around 4500 have found work through the scheme.
Mr Matheson added: "The Glasgow Guarantee is changing lives across the city.
"It has helped thousands of people secure employment or an apprenticeship, but I know we can do more."
The first of the 150 jobs are expected to start with First Glasgow next month.
The posts will go to men and women who have left the services and are registered with the council's Helping Heroes programme, those who are part of the armed forces redundancy programme, and the long term unemployed in Glasgow
Fiona Kerr, Managing Director of First Glasgow, said: "I am pleased that this partnership is proving to be successful in creating full time, permanent employment for these people. We are impressed with the high calibre of candidates applying for the positions
"We want to get more people travelling by bus so we expect a lot from our drivers - excellent customer service skills as well as high standards of driving."