Rhodes, who was dismissed from the Baylor program in June, will sit out the 2014 season and have three seasons of eligibility at Bowling Green.
Bowling Green's new head coach, Dino Babers, coached receivers at Baylor from 2008-11 and intends to install a similar offense with the Falcons.
"Coach Babers talked to him and laid down everything that would be good for him," Robbie's father, Reggie Rhodes, told ESPN.com. "The offense fits him, so there's no transitioning to a new offense; everything is exactly the same. He wanted to go somewhere where he can go in and make an impact and be the No. 1 receiver."
Rhodes, a sophomore, was dismissed from the Bears program on June 23 after multiple drug-related incidents. He was arrested in May on marijuana possession charges, but the McLennan County District Attorney's office declined to prosecute.
Although the charges were dropped, Rhodes was disciplined by the school and agreed to sanctions to remain in good standing with the program. In June, another undisclosed incident violated conditions of that agreement.
"We're exceptionally happy that he had his opportunity to move on in his career," Reggie Rhodes said. "He made some mistakes, but he's going to bury that, put it behind him and move on to be the person and player he's always been."
Rhodes caught 10 passes for 157 yards as a true freshman last season and was the No. 3-rated wide receiver prospect in the country in the class of 2013.