He made just one appearance for Wolves in the Premier League - when he was recalled from his spell at Glanford Park to line-up against Manchester United at Old Trafford in December.
Mick McCarthy, the Wolves manager, had named a deliberately under-strength side for the match - which was lost 3-0 - and were fined £25,000.
Friend had featured in four games for the Iron, making his debut in the 4-1 loss to Blackpool in November and also featuring against Watford, Coventry City and Barnsley.
"Doncaster are a nice Championship club and I am happy to be here," he told Rovers' official website.
"I want to be able to play at the highest level that I can. I wasn't getting many games at Wolves, especially after they got promoted into the Premier League.
"I want to move forward with this club and we have seen from Blackpool that anything is possible in football."