The 25 year old was without a club but has been training with the Blades along with former Barnsley defender David Mulligan. Jagaielka, a midfielder has signed for United until end of the season.
Steve Jagielka Celebrates A Goal!
Steve Jagielka told Shropshire Star "I'm buzzing, I'm absolutely made up," revealed Jagielka, who was the longest serving player having signed during the Jake King era six years ago.
"I've got no hard feelings towards anybody at Shrewsbury because they have been good to me.
"I'm sorry at the way it's had to end but it was probably time for me to move on and get a fresh start anyway.
"I'm going to work as hard as I possibly can to make the most of it."