The 28-year-old turned down a new deal with the Shots earlier this week before leaving as a free agent.
Jones has already worked with Shrews boss Turner during his time at Hereford.
"I think he's a very good defender. He's very strong, very aggressive and he's got enough mobility and pace about him to deal with strikers in the first division," Turner told the club's official website.
"It will be a new experience for him at this level having played in the Conference and then League Two for Hereford and Aldershot.
"Having lost our central defenders Ian Sharps and Shane Cansdell-Sherriff we are delighted to have brought Darren in and I think he will do a good job for us."
