The former Edinburgh captain will arrive at Scotstoun on a two-year contract, strengthening a Glasgow squad set to lose several experienced players at the end of the current season.
Among those departing are Scotland teammates Jack Dempsey, Adam Hastings, and Huw Jones.
Ritchie spent 11 years at Edinburgh after joining straight from school before leaving the club at the end of last season to pursue a move to France. The 29-year-old was appointed captain of Perpignan in his first season and played a central role in their fight to avoid relegation from the Top 14.
He resumed captaincy duties after recovering from a leg injury sustained during Scotland's Six Nations victory over England in February, which kept him sidelined for two months.
Although only a year into his contract in France, a break clause is understood to have enabled Ritchie's return to Scotland without Glasgow needing to pay a transfer fee. Personal reasons are also believed to have influenced the move, with Ritchie keen to be closer to his young family.
Glasgow Warriors will also welcome South African forward Ruwald van der Merwe and Australian utility back Bayley Kuenzle this summer, as head coach Franco Smith continues to reshape his squad.