The 25-year-old defender has signed a two-year contract, with the option of an extra year, and becomes the Addicks' ninth signing of the summer and the sixth since Thomas Sandgaard took over the club last month.
Bowyer said: “It's a position that we needed to strengthen. It has been difficult as there are not many right-footed centre-halves out there but we have managed to get a very good one. Ryan is a winner, it is important when you have players like that at the back, and he's a leader, an organiser and in that centre-half position that is what we were looking for."
Inniss, who represented England at U16 and U17 level, spent more than a decade at Crystal Palace and said he was looking forward to a fresh start with the Addicks.
“I'm glad to get it over the line," he explained. “I managed to train this morning, so I'm super-excited for the challenge ahead. The intensity in training is great, the boys work hard, so it has been brilliant so far."