Rodgers started his career with the Shrews before leaving in 2005 and going on to enjoy spells with the likes of Crewe, Port Vale, Notts County, New York Red Bulls and Portsmouth.
He rejoined Shrewsbury in November, initially on loan from Pompey before completing a permanent move in January, and has since made 15 appearances, scoring twice, although his last outing came over a month ago.
A statement on Town's official website read: "Luke and the club came to an agreement on the remainder of his contract at Town and he has now moved on.
"The club would like to thank Luke for his contribution during his second spell here and wish him well for the future."
- Sports & Recreation