Drivers and technicians had threatened to walk off the job starting at 3am on Thursday following a 24-hour strike on November 19th to protest planned job cuts and an "austerity budget".
But the strike was lifted after management pledged not go ahead with a reduction of staff, media reported.
"We have, I think, obtained a high quality agreement," Valérie Solano, secretary of the SEV union told 20 MInutes newspaper on Wednesday night.
The first streetcar left the Bachet-de-Pesay depot at 4.14am, while the first electric trolley bus left the Jonction depot at 4.22am, the Tribune de Genève reported.
The November 19th strike ground public transport in the canton to a halt forcing commuters to find other ways to get to work.
Taxis were in heavy demand but many people bicycled or walked to their jobs, though others took their cars leading to traffic jams on many streets.
The agreement reached between the two side assures that there will be no layoffs related to the level of services between now and 2018 and no reduction in staff for 2015, the SEV union said.
The deal has yet to be approved by the Geneva cantonal government, which is expected to vote on it on Thursday or Friday, the Tribune reported.
The TPG remains in a financially difficult situation after voters in May backed a proposal to cut fares, which means lower revenues for the transit system.
The government is not prepared to make up the shortfall in revenues and that means service levels are likely to be affected in the coming year.
The TPG tweeted on Thursday that "the network will be served according to the regular schedule".
La grève de ce jeudi 4 décembre n'aura pas lieu. pic.twitter.com/L1lhSN22tO— TPG Genève (@TPGeneva) December 4, 2014