Portsmouth were made to sweat as the transfer window closed without confirmation of the striker's move to the south coast, but the official Spurs website says the deal has gone through after they "reluctantly agreed" to let Defoe leave due to having only 18 months left on his contract.
"I can't wait to be honest. I want to get it done and get my boots on. I'm happy," Defoe told Sky Sports News ahead of the deal's completion.
"For the rest of the season I want to get as many goals as possible, and most importantly get three points and just do well for Portsmouth."
"When you are not playing football you can't expect to get in the England squad," said Defoe.
"I totally understand. I just want to play football and score some goals.
"I want to score as many goals as possible this season and do well for Portsmouth."
Redknapp added: "He will be a great signing for us. He wants to play and he needs to play."
Defoe is set to get the chance to prove himself on a regular basis.
While his future as a regular looked uncertain, a contract extension beyond 2009 remained unsigned and alerted Premier League teams about his possible availability.
"He's too good not to play," added Redknapp.
"He's a fantastic goalscorer, a top player. It will be great to have him here.
"A couple of his mates are here - he's close to Glen Johnson and David James.
"We just keep moving forward as a football club, bringing in better players and moving forward."
Despite his limited opportunities under Jol and new head coach Juande Ramos, Defoe has eight goals this season, including three in as many matches during the Christmas period.