The 30-year-old, most recently with Gillingham, has penned a short-term deal until the end of the season and is available for tomorrow’s trip to Accrington Stanley.
Bennett’s professional career began at Bolton Wanderers and has also taken in spells with Falkirk, Rochdale, Mansfield Town, Peterborough United and Carlisle United.
He joined the Gills last summer, linking up with former boss Steve Evans for the third occasion, and made 23 appearances for the club in that time.
Robinson said: “I am pleased to get Rhys over the line. He is someone that I have had an eye on throughout the season and we have worked hard to secure his signature.
“He is very experienced at this level and was part of a cup-winning side during his time in Scotland (2012 Scottish Challenge Cup).
“Rhys gives us another option in defence. He is a tall, powerful defender that puts his body on the line when needed and I am sure the fans will be looking forward to seeing him in action.”
Bennett becomes the club’s fourth signing of the window, following on from the arrivals of loan pair Bedeau and Trevor Carson, as well as another short-term capture in Ousmane Fane.
Elsewhere, Shrimps’ defender Greg Leigh came off the bench as Jamaica lost 2-1 to Mexico in their World Cup qualifier.
They travel to Panama for their next game on January 30 before hosting Costa Rica on February 2.
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