The 29-year-old has signed a 18-month contract at the west London side after returning to Tottenham from a loan spell with Nottingham Forest earlier this month.
The England international previously worked under Redknapp during the 65-year-old’s three-and-a-half year reign as Spurs manager.
And Jenas is relishing the chance to play regular first-team football in the Premier League after falling out-of-favour at White Hart Lane.
“I’m happy to be here,” said Jenas.
“This is my third deadline-day move. It’s always frantic, but thankfully we’ve managed to get it done.”
He added: “It’s great to be linking up with Harry again. Him being here was key to me making the move.
“I know what he brings as a manager and on a personal level, it’s an opportunity for me to play football.
“It’s no secret I’ve had some injury problems in the last couple of years, but this is a great opportunity for me to play in the Premier League – and hopefully keep this club where they belong.”
Meanwhile, Redknapp believes the former Newcastle United midfielder will prove a key player for QPR in their battle against relegation.
“I know JJ very well, I had him at Tottenham,” said Redknapp.
“I think he’s a good player. He can get from box to box, he’s quick, strong and athletic.
“He’s a good lad with a great attitude. I’m sure he’ll be a big asset for us.”
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