The 34-year-old has now officially signed for the Ligue 1 outfit, joining the club on an initial two-year contract with the option to extend it by a further year.
According to Argentinian journalist Ignacio Miguelez, Messi seriously considered an offer from Atletico to join the club this summer, where he could have played alongside former Barcelona teammate and close friend Luis Suarez.
Atletico head coach Diego Simeone is believed to have been personally in charge of the negotiations, however he was not able to convince the six-time Ballon d'Or winner to join.
Messi has left Barcelona after 21 hugely successful years at Camp Nou, as the Catalan club were unable to re-sign the forward due to their severe financial difficulties.
The Argentine, who will join up with compatriot and head coach Mauricio Pochettino at PSG, is expected to line up in a fearsome front three alongside Neymar and Kylian Mbappe this season.