Rosas, a native of Bogota, Colombia, will become the NBA's first Latino top basketball executive.
Rosas met with Timberwolves owner Glen Taylor on Wednesday and a deal came together shortly after, sources said. Rosas replaces Tom Thibodeau in the Timberwolves' top decision-making position, inheriting general manager Scott Layden and interim coach Ryan Saunders.
Rosas played an immense part with Rockets GM Daryl Morey in constructing a Western Conference championship contender. Rosas has worked 18 seasons with the Rockets and had a brief stint in 2013 as GM of the Dallas Mavericks before returning to Houston. Rosas also works for USA Basketball in a player personnel role.
"Gersson has been an unbelievable person to work with," Morey told ESPN. "He's been way overqualified for his job for a while here. He's more than earned his shot, although I wish he would've gone East. We're going to have an extremely tough competitor in the West.
"Minnesota is going to find how forward-thinking, how hard-working and how talented he is at putting together a winning team."