Workers who maintain trams were due to stage a five-day strike from Sunday in a dispute over pay.
Unite members had claimed that other London Underground workers in the same roles were paid up to £10,000 more a year.
The union said the disparity is causing Tramlink staffing shortages because workers leave as soon as a higher paid job becomes available.
If the talks do not resolve the dispute, strike action will take place from May 5-9 and July 11-15, said Unite.
Unite regional officer Bruce Swann said: “As a sign of good faith, our members have agreed to suspend strike action after Transport for London said it would meaningfully negotiate with Unite over pay disparities.
“Strike action will occur during May and July, however, if a satisfactory outcome is not reached during the talks.”
Navid Golshan, TfL’s general manager for London Trams, said: “We are pleased that Unite has suspended their industrial action by the London Trams engineers.
“This is good news for our customers in south London and we will continue to work closely with all trade union representatives to address concerns and avoid disruption.”
