The 21-year-old joined the Chelsea academy in 2010 but failed to make a single senior appearance for the club, spending time out on loan at Barnsley, Fleetwood Town and Crewe Alexandra over the past three seasons.
Kiwomya has now left Stamford Bridge on a permanent basis, putting pen to paper on a deal which will keep him at the Keepmoat Stadium until 2020.
"I've got good vision and can link up play with my teammates, I've got a lot of pace so hopefully I can use that to create and score goals next season. I spoke to Jordan this week and he was saying that he'd love to come back as he really enjoyed his time here," he told the club's official website.
"The manager puts a lot of time into being able to change formations during a game, the players all work their socks off so I'm looking forward to being a part of that. The main thing for me is getting consistent minutes on the pitch, the manager sees me as an important part of his plans so hopefully I can produce for him.
"I know the club came in for me a couple of times last season but we couldn't get the deal done, it's nice to know they've had their eye on me for a while. It was a hard decision to leave Chelsea as I've been there from the age of 14, but I think it was the right time to make a permanent move and show people what I can do."
Kiwomya scored seven goals in 39 appearances on loan with Crewe last season.