The 35-year-old left Rangers after his contract expired at the end of last season and it is expected he will provide back-up to Julian Speroni as manager Ian Holloway looks to guide the Eagles to Barclays Premier League safety on their return to the top flight.
Alexander, who has three Scotland caps and has also represented Cardiff and Ipswich during his career, stayed at Ibrox last summer despite Rangers' demotion to Division Three, but left the club at the start of the summer and is looking forward to getting to work at Selhurst Park.
"The club did fantastic last year, they've got a great set of players here," he told Palace's official website.
"I've worked with [goalkeeping coach] George Wood before - he's a great coach, one of the best I've worked with. The chance to come back and work with him was very appealing.
"And obviously being in the Premier League, one of the best leagues in the world was one of the main things for me. I'm really looking forward to the season ahead and I can't wait to get started.
"Julian's done fantastically well here. He had a great season last year, but it's important to have good back-up, experienced back-up and I think that's what I'll bring to the squad."
Alexander becomes Holloway's eighth summer signing and joins Stephen Dobbie, Dwight Gayle, Jerome Thomas, Jose Campana, Kevin Phillips, Elliot Grandin and Marouane Chamakh in penning deals with the club.