The midfielder was snapped up on a free transfer from Liverpool in a four-year deal confirmed last night.
Capped 17 times by England - three during Glenn and John Gorman's time in charge - Jamie, 28, has expressed his delight at moving to the Lane after 11 years at Anfield and Glenn reckons he's signed a future Spurs great.
Seen as a great passer of the ball and a 'Spurs' player, Glenn was also quick to underline Jamie's winning mentality and determination.
Glenn said: "He's been captain of Liverpool and is someone who has the highest respect of his fellow professionals.
"I enjoyed working with him and being associated with him when I was England manager.
"He's a very good professional, a diamond lad, a great charatcter and you've got to look at that as well,it's all part of when you buy players, the attitude, the character and with Jamie you couldn't meet a nicer lad.
"With all the fame that he's had and his family as well with his wife Louise, you couldn't meet a nicer guy and he will be a great asset to the club."
In summing up, Glenn simply pointed out that it was a great deal for the club.
"This is very good business for the club," he stated. "It's a very good business deal and, more importantly, it's a very, very good football deal. We're delighted and I'm sure the fans will enjoy watching him."
Glenn Hoddle says Jamie Redknapp's character both on and off the field will be a great asset to the club.