O'Brien made 38 appearances for Leeds after initially joining the club on loan from Bolton Wanderers in October 2010 before later making the move permanent.
However, he was unable to force his way into Neil Warnock's plans in the latter stages of last season and has been allowed to move on from Elland Road.
The 33-year-old has now agreed a deal with Vancouver and the former Republic of Ireland international is looking forward to a new start.
"I'm very grateful for the opportunity given to me by Vancouver Whitecaps FC," O'Brien told the Whitecaps' official website.
"I appreciate the hard work that's been put in by Vancouver, given the short period of time there was to get this deal done.
"I've had the opportunity to look around the city, which is fantastic, and I'm really looking forward to contributing on and off the pitch."
Whitecaps head coach Martin Rennie said: "Andy is an experienced centre-half, who is good in the air and comfortable on the ball.
"He has spent several years in the English Premier League and with some of England's best-known clubs. Andy also had the privilege of being at a World Cup.
"We're delighted to add a defender of Andy's experience to our squad."