Ryan, 22, has signed a two-year contract with the Iron which has the option of being extended into a third season by the club.
"Jimmy is a really good footballer and he is technically strong. He got in the League Two team of the year and has been one of the best players in that division for the last two and a half years," Alan Knill, the Scunthorpe manager, told the club's official website.
"He is progressing. Each year he has got better and better, so that's the reason why we've wanted him at this club. He's at a good age so he's not fulfilled his potential quite yet. He has plenty of it still."
He was out-of-contract at Stanley but the Lancashire club are entitled to a transfer fee as he is under the age of 24.
As the two clubs have not settled on a fee, it is likely to be decided by a Football League tribunal.
Ryan came through the youth system at Liverpool before joining Accrington on a free transfer in 2008.
He made 156 appearances for the club, scoring 25 times, and was named in last year's PFA League Two team of the year.