The 32-year-old, born in Telford, joins Town on a one-year deal following his departure from Championship club Blackburn Rovers.
And Shrewsbury boss Steve Cotterill is delighted to be reunited with a player he has previously coached.
"I've know Elliott for a long time, I had him at Bristol City; I know what I am getting with him," said Cotterill.
"It's five years on since I had him but he's a good leader and a good lad.
"He crosses the ball really well and he's an excellent professional. He will be able to educate our younger players in the dressing room.
"I like to have one or two 'go to' experienced boys around my teams. I am hoping he can come in and be a good influence in and around the team.
"His best position is out on the wide. He can play wide-right or as a wing-back. His crossing ability is great and he can cross with both feet. We are delighted to have him on board and it was very pleasurable seeing him today."
Bennett began his career with Wolves, making two appearances in the League Cup, before going out on loan to Crewe and Bury.
He joined Brighton & Hove Albion in 2009, helping them win promotion to the Championship in 2011 – scoring eight goals as he was named in the League One team of the season.
That earned him a move to the Premier League with Norwich City. Though the Canaries were relegated in 2014, he helped them back up to the top flight through the play-offs 12 months later.
A loan move to Cotterill's Bristol City followed, before joining Blackburn Rovers in January 2016, where he has spent the last five-and-a-half years – helping them earn an immediate return to the Championship with automatic promotion from League One in 2018.