Pochettino has had an encouraging first season at White Hart Lane and Redknapp, who left his post as Queens Park Rangers boss in February, believes that the Argentine is the right man to take the club forward.
Pochettino's main task at Tottenham will be to ensure that the likes of Harry Kane continue to progress, and Redknapp thinks he is the perfect candidate to oversee that development.
"He [Harry Kane] has stepped up this year to a different level," said Redknapp. "He's not a kid who's going to get carried away.
"He's not a 'Billy Big Time'. He'll get on with it, he'll keep practising, keep working at his game and keep improving. He's level headed and is the type of kid you love to see be successful.
"He's well looked after and in good hands. I like the manager at Tottenham, Mauricio Pochettino. He's a good manager and a lovely guy."
Kane's 29 goals this season have fired Tottenham up the league and have been a major reason behind Pochettino's success, but the 43-year-old boss still deserves credit.
He showed the faith that other managers haven't had in Kane by putting him into the first-team, and is now reaping the rewards.
Kane is not the only youngster to break into Tottenham starting line-up under Pochettino, either.
The striker has been joined by Nabil Bentaleb and Ryan Mason, who have also made the step-up from the academy, and the hope is that more will follow in the future.
Spurs currently have a very exciting crop of youth team players coming through and will be hoping to see some of their more exciting prospects break into the senior squad next season.