Following their title triumph, owner Sanjiv Goenka had informally announced that the ATK prefix was finally going away after three years.
Locked 0-0 in the first leg, the reverse fixture also saw a goalless stalemate till 120 minutes of play, including regulation and extra time.
After a goalless first-half, the Mariners took the lead through a 68th minute strike from Slavko Damjanovic.
Griffiths played a vital role for Mumbai City FC in their successful run last season with 28 tackles, 14 interceptions and 43 clearances in 17 games.
Goals from Hugo Boumous and Dimitri Petratos were enough to end Odisha FC's first ever playoff run and secure semi-final qualification for the Mariners.
Goa has been chosen for the marquee match due to the availability of training grounds and other infrastructure for the teams.
A win for the Mariners can hand them their maiden ISL title, while the Blues could lift their second one, having last done so in the 2018-19 season.
After the drawn match, ATK Mohun Bagan moved up to fourth place in the standings, but remained just three points clear of the sixth placed team.
"Martins will start training for the club from Tuesday," ATK Mohun Bagan said in a statement.
Here are the streaming details for the Indian Super League match between Kerala Blasters FC Vs ATK Mohun Bagan Football match.
Hyderabad FC entered final despite 1-0 loss in second leg as they had already won the first leg 3-1 against ATK Mohun Bagan.