The 36-year-old has agreed to join Hearts as a player-coach from 1 July when his current contract with Crystal Palace expires.
Alexander will add some experience to Robbie Neilson’s squad as Hearts attempt to return to the top tier of Scottish football at the first attempt.
And the former Livingston, Ipswich, Cardiff and Rangers goalkeeper is relishing the prospect of combining coaching and playing with the team he supported as a youngster.
Alexander said: "As a boyhood Hearts fan, I am delighted to get the chance to join a club I have supported for many years. With the coaching side of it as well, this is a fantastic opportunity for me.
"I'll be signing on July 1. I'm excited at the challenge ahead, am raring to go and delighted to be back in Scotland.
"At 36, I need to start looking to the future and want to get involved in coaching.
"The club has given me a great chance to get a foot on the ladder and it's an opportunity I just couldn't turn down.
"We have a young squad and if I can help bring on these kids, hopefully it will work well for us all."
Hearts start the new campaign with an away match at newly promoted Rangers, and having spent five years at Ibrox, Alexander is looking forward to playing at the ground again.
"With the fixtures now out, it really gives you an incentive to be involved in the first game," Alexander said. "It's a really exciting start for us and I definitely want to be involved on 9 August.
"This club has fantastic supporters and their backing has been phenomenal. Hopefully we can give them something to cheer about after what has been a very difficult 12 months for everyone at the club.
"If we can get a good team on the pitch and season tickets keep going well, hopefully we can bring a lot of success to Hearts."
Alexander is the fourth arrival at Hearts in recent weeks, with James Keatings, Soufian El Hassnaoui and Morgaro Gomis also joining the club.