Rangers had pulled out of a deadline day swoop for Townsend earlier on Thursday, but the midfielder has now completed a move to the club until the end of the season.
Redknapp told the club's official website: "Andros is a kid with a fantastic future.
"I like Andros an awful lot. He's a winger, he's strong, he's quick, he's brave and he scores goals. He's unlucky that he's got [Gareth] Bale and [Aaron] Lennon keeping him out of the team.
"I think eventualy he'll become a big player."
Townsend stated that the move to QPR was a "no-brainer" after finding out his former manager Redknapp was interested in signing him.
"I worked with Harry at Spurs - he gave me my debut - so it was a no-brainer when QPR came in for me," Townsend added.
"Harry has brought me in to do a job for him. I'm confident in my own ability and I want to repay him. I live for pressure games. I'm looking forward to the challenge.
"I've learnt a lot through my loan spells in the past and now I'm at a massive club like QPR and I'm confident I'll do well.
"I'm relieved the deal is over the line. It's all happened quite quickly, so I'm just excited about the weeks and months ahead."
Jenas arrived at Loftus Road earlier in the evening and has agreed an 18-month deal that severs his ties with Spurs.
QPR pulled the plug on a planned triple Spurs swoop for Jenas, Townsend and David Bentley this morning after being put off by Tottenham chairman Daniel Levy's demand that the relegation strugglers take all three players or none at all.