New Zealander Ryan, who led his country at the World Cup in South Africa in 2010, was released by Rovers after the club agreed to the termination of his contract
Spurs boss Harry Redknapp had been keen to bring in another defender after Sebastien Bassong joined Wolves on loan for the rest of the season on transfer deadline day.
Tottenham watched Nelsen in a reserve game against Huddersfield on Tuesday prior to Rovers cancelling his contract.
He has only played one first-team game this year, but assistant manager Kevin Bond revealed that the veteran will be in the Tottenham squad for Monday's Barclays Premier League game at Liverpool.
"He is fit and eligible to play on Monday," Bond said. "I've just had a cup of tea with him in the canteen. He is looking forward to the challenge."
Source: PA
Source: PA