The winger put an end to speculation about his future by penning the deal on Friday morning and he will now stay at Tottenham until 2014.
Lennon had been linked with a move to Liverpool but Redknapp maintains that he was always confident of keeping the 21-year-old.
"He has signed an extension to his contract and he is here for the next five years, which is good news for the club," Redknapp said on Sky Sports News.
"He wants to stay and we want to keep him. We'd had no enquiries anyway.
"He is a young player with a great future. He has been fantastic since I've been here so we are delighted to have secured him long-term."
Redknapp is excited about Lennon's potential and has tipped him to improve considerably as his career goes forward.
"He has got all the ability, he's so quick," said the Spurs boss. "But he's still learning and he's not the finished article yet.
"If he keeps listening and learning he could go on to become a fantastic player."