The Brazilian midfielder has 98 Premier League appearances to his name but had dropped down to the Championship following QPR's relegation last season
The Premier League club confirmed on Friday that the Brazil international, who last played for his country in 2012, has undergone a successful medical and joined them until the end of the season.
West Brom have the option to make the move a permanent one at the end of the campaign.
"I spoke to the manager and was impressed," Sandro told the club's official website. "This is a big club and I feel happy to be here and very happy to be back in the Premier League.
"I believe I have a lot to offer. It was my first day today and I am looking forward to being part of this family.
"As a player I play with my heart, I give all I can on the pitch - all the time I want to win the ball and play the ball. I hope the fans will see the best of me during my time."
Sandro has 98 top-flight appearances to his name between his spells with Tottenham and QPR, who were relegated to the Championship last season.
West Brom boss Tony Pulis added: "We are delighted to bring such a quality player to the club.
"We have got a few injuries and knocks at the moment so we are pleased to be able to strengthen the squad. Sandro has a great pedigree and will be a good addition."