And the boss reckons the England international could be the 'steal of the decade' after grabbing his signature on a free transfer from Liverpool.
The deal to bring the midfielder to the Lane went through earlier this evening. The 28-year-old has signed a four-year contract after serving the Reds, often as skipper, for over 11 years.
Glenn beamed: "We're absolutely delighted to have him on board. He's a class player, one I had in the England squad when I was manager, an excellent professional and he's joined us on a free transfer.
"I'm sure Spurs fans out there, within four months of next season when he's settled and playing, they'll be saying he's one of the best signings the club has made - especially on a free transfer.
"In today's market you are talking six or seven million pounds because he can pass the ball and he can play.
"He's a Spurs player, a player in the style and traditions of the club and I'm sure the fans will enjoy watching him."
Glenn said we had beaten off the interest of a few other clubs to bring Jamie to the Lane.
He revealed: "We wanted him, he wanted to come, Liverpool kindly said we could talk to him, they knew he was out of contract at the end of the season and they offered him a good contract to stay.
"We've beaten off a few other clubs and Jamie wanted come here.
"He's delighted to be here and we're delighted to have him. He will be a major, major influence on us taking the club forward."
Glenn was naturally aware of Jamie's injury problems but was confident he was over them.
He added: "He's had a few injuries and we had to be aware and monitor that. I'm confident he's over them.
"In many ways, I was asked the same questions about Darren and Les at the start of this season and I think Les has had his best season since he's been here and Darren the same, he's almost got himself into the World Cup squad.
"There are similar things that we will be working on with Jamie and we've already spoken about them. Let's see what happens in 12 months - he could be the steal of the decade."
Glenn Hoddle believes he's signed a future Spurs great in Jamie Redknapp.