Evans, a former Wales Under-21 international, joins the Saddlers on a two-year deal.
The 25-year-old spent most of last season as Cheltenham's first-choice shot-stopper, having made 27 league starts.
“I think it is a new team being put together and I am really excited to be part of it," said Evans.
“I am looking forward to the season and what it brings for the team.
“I am looking forward to pushing the reset button, starting fresh and giving myself a good platform to go off and continue in my career.”
Evans has also had spells at Wigan Athletic, Sutton United and Macclesfield Town.
He is Michael Flynn's ninth signing of the summer.
“Owen is a very talented goalkeeper,” added Flynn.
“He’s played in League One with Cheltenham, had good experience with Wigan, been with Wales Under-21s and has the potential to kick on.
“He showed a real desire to come to the football club and is eager to do well.”