The Goan defender won the recently concluded edition of the ISL with Chennaiyin FC but has decided to shift bases to Pune.
Almeida made only four appearances for the Marina Machans in the 2017-18 season as Spaniard Inigo Calderon was largely preferred at right-back by coach John Gregory.
The 26-year-old was a part of FC Goa in the 2015 and 2016 seasons of the ISL and the Stallions will be his third ISL team.
FC Pune City have already signed winger Nikhil Poojari and are in advanced talks with Bengaluru FC's Alwyn George. The former Sporting Club de Goa defender is their latest recruit as the team from Pune start preparing for the next season in earnest.