Nelsen, who has made 21 appearances for Rangers this season, was given time off by manager Harry Redknapp to travel to Canada for talks with Toronto and the deal has now been confirmed.
Redknapp, who signed the defender when Tottenham manager, said earlier: "Nelsen is very important to us, a fantastic leader, a top player.
"He has been offered a job in America and I think there is every chance he might want to go.
"He wants to be a manager and it is a chance for him to manage a club.
"He has been fantastic. I took him to Tottenham last year from Blackburn. He's one of the best pros I've ever met in my life, a fantastic player, a great trainer.
"He is a massive part of your team. To lose him would be a massive blow for us."