Spurs were awaiting international clearance after agreeing terms with the 34-year-old New Zealand captain, according to his agent.
Lyle Yorks, Nelsen's Washington-based representative from James Grant Sports, told the Washington Post: "We settled with Blackburn and have reached agreement with Spurs. We're just awaiting clearance. It's for six months, with a one-year option. It all unfolded quickly."
Nelsen, who is able to sign for a new club outside the transfer window because he is now a free agent, was in the final year of his Rovers deal and had had made just one appearance since April following a knee injury.
His move to Tottenham is something of a surprise considering that and his age, as was the north Londoners' swoop for Everton striker Louis Saha just before the January transfer window shut.
The pair will fill the void left by the departures of Sebastien Bassong, who joined Wolves on loan, and Roman Pavlyuchenko, who was on the brink of completing his reported ?8million move to Lokomotiv Moscow.
The Russian transfer window is still open, so Pavlyuchenko did not need to wrap up the formalities of the deal on Tuesday night, with Lokomotiv confirming only a medical remained to be conducted.
Source: PA
Source: PA