It is Redknapp's second signing of deadline day after completing the record signing of Chris Samba earlier in the day
Jenas joined Tottenham from Newcastle in 2005 for a fee of £7million and went on to make over 200 appearances for the North London club before falling out of favour.
A season long loan at Aston Villa during 2011/12 was cut short by a serious Achilles injury that kept him out for six months but despite a change of managers at White Hart Lane he could still only manage one appearance under Andre Villas Boas.
The 29-year old was sent out on loan to his first club Nottingham Forest in September and made six appearances.
He will now be hoping to revive his career with a move across London to help QPR's fight for survival.
And he admitted linking up with Harry Redknapp was a big persuasive factor in his move to West London.
He said: "Obviously the fact that Harry was here made a big difference. He knows me well as a player.
"There's a big challenge ahead and I want to be a part of it. There's no time to waste, we need to hit the ground running and get the wins, starting on Saturday."