The 34-year-old, who spent the closing weeks of the season on loan at The Valley, has signed a one-year deal following his release from Swansea.
"Mark is a player who came in towards the end of last season and, after initially having to wait for his chance, made a real impact in the final few games," Powell told the club's official website.
"He offers us good experience in the middle of the park, is a good user of the ball and has played in the Premier League with Swansea.
"He's a player I've had my eye on for a while, even before he joined us on loan, and he adds to the competition for places in midfield.
"Along with the likes of Andy Hughes, who signed a new contract last week, he's another good character and I'm very glad to have him on board for next season."
Gower, who arrived on loan from Swansea in March, made three substitute appearances before starting the last two games for Charlton.
He spent the previous four seasons with Swansea and made 21 appearances in the Barclays Premier League.