The 25-year-old was a free agent having made 35 appearances for the Daggers last term, which proved to be the final year of his six-year stint with the club.
“There were a few clubs involved and I wanted to take my time and make sure I made the right decision,” he told the Shrews’ official website.
“After having a chat with the manager, I went home, thought about it and feel I have made the right decision.
“It will be the first time I’ve moved away from home but it will be a good experience. I was at Dagenham for six years and thought it was time in my career that I moved on.
“I started off there as a right-back but have played in midfield in the past few seasons. I’m still only 25 but I’ve played over 250 games now.”