PSG, backed by Qatari billionaires, said Cole, 31, who is yet to sign a contract extension at Stamford Bridge, will join the club next summer. The announcement was made on the club's official Twitter account.
However, the tweet which said, "English left back Ashley Cole will become a Red and Blue player this summer" was immediately deleted.
The England left-back is certain to leave the club with the Blues' policy of offering not more than 12 months contract to players above 30, which includes veterans like midfielder Frank Lampard and defender John Terry.
Lampard, 34, has been linked with a Chinese club and LA Galaxy in the MLS. Even new interim manager Rafa Benitez has said the England duo could leave next summer but was not sure about their future at the club.
Both Cole and Lampard will see their contracts expire in seven months time and free to sign pre-contract deals with clubs next summer if they do not agree any contract extensions.
Lampard, who joined Chelsea from West Ham united in 2001, has 93 caps for England and is the club's third all-time goal-scorer with 189 goals from 571 appearances. The 34-year old midfielder has won three Premier League titles, four FA Cups, two League Cups and the UEFA Champions League.
Cole, who has 99 caps for England, has won the Premier League title once, FA Cup four times and the Champions League since joining Chelsea from arsenal in 2006.