The 35-year-old New Zealand captain has been a key player for QPR this season, playing 21 times in all competitions since joining the club in June.
The defender will still be available for the west London club's Premier League match against Tottenham Hotspur on Saturday and wants to talk to Rangers manager Harry Redknapp to discuss when he will join up with his new team.
"This was too great an opportunity to turn down," Nelsen said at the news conference.
Nelsen spent four years in the MLS playing for DC United between 2001 and 2005. (Writing by Toby Davis in London; editing by Tony Jimenez)