Nelsen, 34, said the switch to the London club, arranged on the final day of the January transfer window, was an "absolute no-brainer".
"It's just an exciting opportunity at this stage of my career," he told the Christchurch Press. "I've loved my time at Blackburn but it's something I just couldn't turn down."
Nelsen said Tottenham manager Harry Redknapp had offered him a six-month contract with a one-year option because he wanted experienced defensive cover at Spurs, who are third on the Premier League table.
The New Zealander, who has been sidelined for much of the season with a knee injury, said he had some minor visa issues to finalise but the deal was "pretty much done".
Nelsen captained New Zealand at the 2010 World Cup, where the All Whites were the only team to remain undefeated in the pool stage but still failed to advance to the knockout phase.
The Blackburn Rovers website confirmed Nelsen had been released after the player and club agreed to terminate his contract, describing him as a firm favourite with fans during his time at Ewood Park.
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