Nelsen was a surprise signing by Spurs boss Redknapp after the defender was released by Blackburn in January.
Injury had restricted the 34-year-old to just one appearance this term before his move to White Hart Lane and although he has yet to start a Barclays Premier League game for his new club, he has played a key role in their run to the FA Cup semi-finals.
Tottenham are the bookies' favourites to end their 21-year wait for cup glory while they still have a chance of finishing third in the league for the first time since 1987.
"That is a far cry from the position relegation-threatened Blackburn were in when Nelsen left.
"I'm just so glad the manager gave me an opportunity in January to come here and trying to help out as much as I can and do the best for the club," Nelsen said. "I've played in some really good Blackburn sides. We finished sixth and seventh in the league when I first got there.
"But, I've got to admit, the quality of players is fairly phenomenal over here - playing alongside them is a real privilege."
He added: "This opportunity came up and I wanted to repay Tottenham and Harry for bringing me in."