Purdue announced Marve would become a Boilermaker in a news release Thursday. Coach Danny Hope said Marve immediately made Purdue a better football program.
Marve's high school coach, Robert Weiner, said last week that Marve was considering walking on at Tennessee.
Marve completed 116 of 213 passes for 1,293 yards with nine touchdowns and 13 interceptions last season for Miami.
He missed his freshman season because of injuries from a car crash. He split time last season with Jacory Harris, but was held out of the Emerald Bowl after missing class.
Marve won't be eligible until the 2010 season.