Rangers announced that Zarate has signed a deal until the end of the 2014-15 season and is in line to make his debut against Burnley in the Premier League this weekend.
Redknapp told the club’s website: “We’re really pleased to bring Mauro in. He’s a good footballer, someone with great ability who can play as a No 10.
“I first saw him when he was on loan at Birmingham quite a few years back and I actually tried to take him to Portsmouth back then.
“He’s a more-than capable player, he’s already shown that, and hopefully he can come in here and do well for us.”
Zarate added: “I am happy – I need this.
“I need to play and Queens Park Rangers have given me this chance to show what I can do. The Premier League is the best in the world at this moment. Does my style suit the Premier League? Maybe. We will see.
“When I met the manager he told me he wanted to sign me for Portsmouth before, but in that moment I went to Lazio. But now I am here and will play for him.
“I will try to do different things with the ball, some skills to make the difference for the team, for me and for the other players. I am fit and I hope I can be involved on Saturday.”