The pair have put pen to paper on new one-year deals at Roots Hall.
Barker, 32, admits he is now determined to help the club get promoted from npower League Two after they exited in the play-offs last season.
"Last season is old news now and we have signed some good new players," he told the club's official website.
Leonard, 20, suffered an injury-hit campaign in the latter part of the season but is keen to impress once competitive football returns in August.
"I really like it here and I have enjoyed my time here," he said. "Now I want to build on what I did last year and try and establish myself as a regular starter."