The 27-year-old moves to Glanford Park on a Bosman after making more than 300 appearances for the Shrimps.
He said he was convinced to make the move to North Lincolnshire after meeting with the Iron boss Nigel Adkins.
"He was passionate about getting this club back into the Championship and I want to be a part of it," he told the official SUFC website.
"The manager really impressed me and, overall, it was an easy decision."
He has penned a three-year deal with The Iron and will officially become a Scunthorpe player on July 1.
Thompson scored eight goals in 42 appearances for Morecambe this season.