The Spurs manager had been widely touted to succeed Fabio Capello as England boss at the end of the season before the shock appointment of Roy Hodgson this week.
And, now that the north London club will no longer be forced to replace Redknapp in the summer, Van der Vaart has underlined his desire for the 65-year-old to enjoy a lengthy stay.
"I am happy he is staying," the 29-year-old told reporters.
"He is doing a fantastic job here and it's important for any club that a manager stays as long as possible, especially here.
"It's his fourth season and every year he has done well, so I think everybody is happy about it. He is a special manager.
"He always gives you a lot of confidence and it is not as though he is on your case the whole time.
"He talks with the players so we are really happy with him, and you could see in the game last night that we wanted to fight for him.
"The England situation wasn't a problem. We read the papers and knew he could go to the national team at the end of the season but for us it has not been a problem.
"Sometimes you just have bad luck - like losing the semi-final against Chelsea with that goal that wasn't a goal.
"We have been unlucky and I hope the luck is back."
Tottenham's 4-1 defeat of Bolton on Wednesday night sees them fourth in the Premier League, ahead of Newcastle on goal difference and just one point behind neighbours Arsenal.
And the Dutchman is keen to ensure that his side keep hold of their position, in order to secure a return to the Champions League.
"We look to Arsenal - we were 10 points ahead, now we are one down, but anything is possible," he added
"As long as we win, I have a feeling we will be in the Champions League."
Should London rivals Chelsea fail to finish in the top four - as is looking increasingly likely - they could take England's fourth Champions League spot with a win against Bayern Munich in the competition's final later this month.
That would mean that Spurs' efforts this season have been in vain but the former Real Madrid man says his side must concentrate on their remaining fixtures.
"I hope my friends in Germany do a good job!" he added.
"We want to win every game now and we will see what happens. A win is always a medicine. When you win everybody is happy.
"We played a good home game against Blackburn [2-0 win on Sunday] which was important.
"Then we go to Bolton, where it is always difficult to win, and win 4-1 - the confidence is high. But the next game [away to Aston Villa] is going to be really difficult again."