The striker, 19, has scored 10 times in 38 league appearances for the Uruguayan club and will now move to Europe to continue his development.
Rolan arrives at Bordeaux as a replacement for Yoan Gouffran, who last week secured a move to Newcastle.
"This will be a good signing for us," coach Francis Gillot said. "He is a young player but one with a future.
"I didn't know him, but our scouting department have seen him six or seven times. I have watched him on DVD and I have faith in the scouting department because they did a good job last season."