Kiwomya, who has signed a three-year deal, spent last season on loan at Doncaster and helped them earn promotion from League Two under manager Darren Ferguson.
The 21-year-old never appeared for Chelsea's first team but won the FA Youth Cup and UEFA Youth League with the Blues.
He said: "I know the club came in for me a couple of times last season, but we could not get the deal done.
"It is nice to know they have had their eye on me for a while.
"It was a hard decision to leave Chelsea as I have 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.
"I spoke to Jordan (Houghton) this week and he was saying that he would love to come back as he really enjoyed his time here."