Trade unions Unite, GMB and Siptu had announced they would take the action between Tuesday and Thursday, February 27-29.
But following crunch talks on Sunday, February 25, the unions said they had received an improved pay offer from Translink.
The three public transport unions said they will now ballot their membership on the new offer.
In a statement, they said: “Pay negotiations between the transport unions and Translink management were reconvened today [Sunday] following the rejection of an initial pay offer by management on Thursday [22 February].
“Following the receipt of an improved pay offer for all Translink employees workforce reps suspended the planned 72-hour strike action set for 00:01 on Tuesday (27 February).”
The outcome of the ballot is expected to be known later this week.
Infrastructure Minister John O’Dowd welcomed the suspension of the strikes, describing it as a “positive development”.
Mr O’Dowd said he wanted to thank the unions and Translink management for their “determination to find a resolution to this dispute”.
The minister said that resolving public sector pay quickly “has been a key priority” for the newly-formed Stormont Executive.