The TSSA is smaller than both the RMT and Aslef unions, which are still in dispute with the rail companies over pay, job cuts and changes to terms and conditions.
The TSSA said that the two-year pay deal would mean a 5% increase in 2022, 2023 or a minimum of 1,750, and a further 4% the following year.
It has secured commitments on job security and full consultation over any possible changes to terms and conditions. The deal is in exchange for staff accepting changes to working practices - including a new multi-skilled station role.
There will be no mandatory redundancies among certain staff, including station workers and all on-board staff, until the end of 2024, according to the agreement.
A spokesman for the Department for Transport said the outcome was positive and that it allowed the vital reforms needed to get railways back to a financially sustainable footing. Members of the RMT union from 14 train operators are due to strike on March 18, 18 and 30 March and 1 April, which marks the start of the Easter school holidays for many.
The TSSA was set to make a breakthrough after the RMT executive rejected an equivalent offer last month and refused to put it to members in a vote.
Steve Montgomery, Chair of the RDG, said: We hope that the RMT leadership will take this opportunity to reconsider their rejection of our equivalent offer, call off their unnecessary and disruptive strikes, and allow their members to have a referendum on their own deal.