A talented prop, who can play both tighthead and loosehead, Morris then moved to Newcastle Falcons where he made 42 appearances in the past two seasons.
Commenting on the province's latest acquisition, Connacht Rugby CEO Gerry Kelly said: "Robbie will bring a lot of quality and strength to our side. He is a very good signing and his experience will be extremely valuable to our younger players.
"It is another significant signing at a time of change for Connacht and with another few signings to be announced in the coming weeks, it promises to be an exciting campaign next season."
Newcastle's director of rugby John Fletcher said: "Connacht represents a new challenge for Robbie, and it should allow the opportunity for the regular first team rugby which is so important to his own continual development."