"This was too great an opportunity to turn down," Nelsen told a news conference.
The 35-year-old New Zealand captain has been a key player for QPR this season, playing 21 times in all competitions since joining them in June, and is still under contract to the Premier League's bottom club.
Nelsen will be available for QPR's league game with his former club Tottenham Hotspur on Saturday and wants to talk to Rangers manager Harry Redknapp to discuss when he will join up with his new team.
The defender spent four years in the MLS with D.C United between 2001-05. He then had a seven-year spell with Blackburn Rovers before joining Tottenham.
"From the day Ryan arrived in Washington D.C as a 23-year-old I always knew he would be a head coach someday," Toronto president and general manager Kevin Payne said on the club website.
"I believe his leadership qualities, intelligence, preparation and character will contribute to his success as a coach. I couldn't ask for a better person to lead our club."
Nelsen replaces former England and Arsenal striker Paul Mariner who was sacked on Tuesday after seven months in the job.
"This was a difficult decision but one that was made in consideration of the strategic and cultural direction our club is taking," Payne said.
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