The 30-year-old left the club in 2005, returns initially on loan, but that will become permanent when the transfer window opens in January.
Rodgers, who scored 65 goals for the Shrews in his first spell, will go straight into the squad for the trip to Leyton Orient.
Boss Graham Turner told the club's official website: "He's obviously a goalscorer and people around Shrewsbury Town know him well enough. He was a very popular character when he was here first time.
"He's gone off and got a lot of experience. I'm told he's quietened down a little bit now from his early days but I just think his movement and his goalscoring ability might spark something in the penalty area for us.
"It's obviously been a weakness so far this season, the number of goals we've scored. I'm hoping Luke will just add that expertise in and around the penalty area with his movement."