The 23-year-old has reportedly signed a five-year contract with his new side, who qualified for the Champions League in fourth place after Ligue 1 was prematurely halted due to the worldwide pandemic.
He joins from Lyon, who finished down in seventh.
Lyon previously purchased Terrier from Lille for a fee of €11m, with him subsequently going on to make 55 appearances over two seasons for Les Gones, scoring 17 goals.
Rennais F.C. (@stadeRennais) July 7, 2020
He made just 13 starts in the league for Lyon, with him unable to consistently break into the starting XI to become a key player under head coach Rudi Garcia.
Terrier’s outings in Ligue 1 this season earned him a 6.3 FC Rating. Usually deployed as a left winger by Garcia, he averaged 1.2 dribbles completed per game and 1.7 completed crosses per game, as well as 3.2 touches in the opposition box per 90 minutes.