Severn, 20. is a free agent having been released by Championship side Derby County this summer.
He trained with the Iron in the closing stages of the season after it became clear his Rams contract would not be extended.
"We had him in through the season and we liked him a lot. He's a modern goalkeeper – six foot and really athletic – and he wants to come here and be better," Alan Knill, the Iron manager, told the Scunthorpe Telegraph.
Severn's only first-team appearance for Derby came in February 2011, when he came off the bench after 47 minutes of the 1-0 Championship loss to Hull City.
He has also had loan spells at Tamworth and Eastwood Town, and has represented England at U17, U19 and U20 level.
Knill has already told Sam Slocombe, who swept the board in the club's player of the season awards, that he will remain as the club's first choice keeper going into next season.