Rovers have been in talks with the 22-year-old for several weeks and compensation is yet to be agreed with the Bees due to his age.
However, the former Aston Villa man has expressed his delight at finally pushing his move to South Yorkshire through.
"I'm very excited to be here, I've been here a while now and have got to know the lads and the manager and I'm really excited for the season ahead," he told the club's official website.
"As soon as I met Paul [Dickov] and John [Ryan] it became a no brainer for me; I spoke to my agent straight away and told him I thought Doncaster is the place for me.
"The deal was done a couple of days after that and now I'm just really happy to get things going.
"There's a good core to the team here, we will have to add a couple of new faces which I'm sure the backroom staff are looking at now.
"The team and players that we have got here at the moment are good enough but with further additions we can give it a real go - it's not going to be easy but we have got to enjoy it."