The Brazil international has signed a three-year deal at Loftus Road after a fee was agreed with their fellow Premier League club earlier in the day.
Sandro, 25, made 60 starts in his spell at White Hart Lane but had not been involved in any of their games so far this season with new boss Mauricio Pochettino preferring other options in the Tottenham midfield.
Boss Harry Redknapp, who originally signed Sandro for Spurs, said: "Sandro's a proper footballer and a top class professional - he's an absolutely fantastic signing for us. I couldn't be more pleased.
"He's been a massive target of mine all summer and I honestly didn't think we'd be able to pull it off - it's a real statement from the club, from the owners, to bring in a player of his undoubted ability.
"He brings energy, aggression, power and quality. They call him the Beast. He's not only a top quality footballer, but a fantastic boy as well. He'll lead by example for us. Tottenham fans loved him and I'm sure the QPR fans will too."
"I like new challenges and this is one I'm really looking forward to," said Sandro.
"Working with Harry again, who I share a great relationship with, is very special to me. Football is in my heart and I'm very happy at this moment. I'm very pleased to be here and I'm looking forward to meeting my team-mates.
"I had a good relationship with the fans at Tottenham Hotspur and I will try my hardest to get the QPR fans to like me. I will give everything on the pitch and fight for every minute. I'm ready and raring to go."