Jason Rust, councillor for Colinton and Fairmilehead, had urged the sport and leisure provider to introduce free access.
Edinburgh Leisure's Board has now agreed to allow those who are categorised as having a disability as a result of serving in the forces concessionary rate access.
Cllr Rust said: "After a few months of to-ing and fro-ing, a concessionary rate has been agreed and will be in place from New Year's Day.
"I am pleased they have taken on board the points raised and while they have not gone for free access, they are following the path already adopted in other local authority areas.
"A substantial number of residents will benefit from this decision."
In a letter to Cllr Rust, Keith Jackson, chief executive of Edinburgh Leisure, said: "We believe that there are in the region of 1,800 ex-service people in Edinburgh who may be eligible for this concession."