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."