The 27-year-old who made 5 appearances for Liverpool under Brendan Rodgers and Jurgen Klopp left the club to join Rangers in 2016 before moving on to Bury, Fleetwood Town, then Joey Barton's Bristol Rovers in 2022.
After his end-of-season departure from Bristol Rovers he had been on trial at Oteley Road for some time and played two pre-season games for Shrewsbury where he impressed.
Rossiter joins Luca Hoole and striker John Marquis and the clubs third signing of the season and Shrewsbury boss Paul Hurst is proud to get him on board.
“Jordan came in on trial but we knew it was never going to be a long trial," said Town boss Paul Hurst. "Fitness has been his issue but he has come through the games without any problems. He could be a really big player for us.
"He has got a really good pedigree. He's been with Liverpool. He went up to Rangers as well. He had a really good start to his career and he is the type of player that will have gained a lot from those experiences. He is a genuine lad."