The former Rovers captain said he had made "life-long friends" at the Lancashire club.
"It's been a fantastic time in my life."
He said his former teammates had wished him the best.
Nelsen's American agent Lyle Yorks said they were waiting only on an international clearance.
Blackburn dramatically cancelled Nelsen's contract just moments before the window closed, which made him a free agent and gave Spurs more time to sign him. The 34-year-old's contract with Blackburn was due to expire at the end of the 2012-13 season.
"We settled with Blackburn and have reached agreement with Spurs," Yorks told the Washington Post.
"We're just awaiting clearance. It's for six months, with a one-year option. It all unfolded quickly. Harry Redknapp has always been a big fan of Ryan. When the opportunity came up, it really played itself out today."
It's not a move that's universally popular with both Spurs and Blackburn fans, with Tottenham fans in particular pointing to Nelsen's age and struggles with injury. He hasn't played a competitive game since Blackburn's 3-1 defeat to Aston Villa on August 20 and recently returned to New Zealand to have his knee injury assessed by All Blacks medical staff.
But when fit - and it's widely believed he will return soon - he is one of the best defenders in the Premiership. He proved that at the 2010 World Cup, when he helped the All Whites to draws against Slovakia, Italy and Paraguay and was chosen in many pundits' team of the World Cup.
Spurs have skipper Michael Dawson, Ledley King and Younes Kaboul on their books at centre-back but King is injured more often than not and Dawson has also had injury problems. French defender William Gallas is out with a long-term injury and Tottenham yesterday offloaded Sebastien Bassong to Wolves.
"I'm hoping to sign Ryan Nelsen on a free until the end of the season," Redknapp said after his side's 3-1 defeat of Wigan yesterday (NZT) that solidified their third place in the Premier League. "I think he's a great competitor and a good sort to have at your club. Always liked him."
Redknapp tried once before to sign Nelsen when he was Portsmouth manager but the All Whites skipper proved difficult to prise away. Nelsen was also linked to a move to Arsenal about five years ago but this proved little more than paper talk. There have been many who wondered how he would fare at a top-four club and, while he's not now in his prime, will soon get a chance to see.
"Tottenham are right up there with the big guns, so it's fantastic for Ryan," said former All White and Oceania Player of the Century Wynton Rufer. "Ryan is international class. Unfortunately we don't have that many players playing that level and to go one step higher, all credit to him."
Nelsen has played more than 200 games for Blackburn and been a big reason for their continued existence in the Premier League.
He also earns close to $8 million a year, making him the highest-paid sportsman in the country, which might have been one of the reasons Blackburn were happy to offload him.
