First Glasgow was facing the threat of walk outs by workers in a dispute over pay.
The Evening Times revealed last week that the firm upped their offer after staff decided to strike.
The engineers rejected a 1.2% pay rise in each of the next two years by 98 votes to 15.
Management then agreed to up their wages by 1.8% a year.
Trade union Unite held a fresh ballot and 52% of staff accepted the offer.
The deal ends the dispute which began when First initially offered a pay rise of just 0.5%.
Unite Regional Industrial Officer Eddie Duffy said: "We were clear in our belief from the very outset that First could find more to meet our members'
aspirations for a decent pay increase and ultimately we've been proved right - 3.5% over two years is a significant
mark-up on the initial offer of 0.5%.
"Thankfully the prospect of disruption to bus services across the city during the
Commonwealth Games has been avoided but the management at First Glasgow should be asking themselves why they left it until the eleventh hour to produce a basic offer that could and should have been delivered months ago."
Managing director of First Glasgow, Fiona Kerr, said: "I'm pleased that we've successfully resolved this dispute and that our customers will be spared any inconvenience that might have been caused by industrial action."