The 44-year-old was working as Tottenham's Under-23 coach when he collapsed at the club's training ground yesterday before being rushed to hospital.
It later emerged that the former Aston Villa defender suffered a cardiac arrest and died on Friday morning, prompting an outpouring of sympathy from the football world.
"This is an incredibly sad day for the club and a tragic loss of a talented member of our Spurs family," read a statement from Spurs chairman Daniel Levy.
"Ugo was an extremely popular and respected academy coach, a tremendous influence on our younger players both in training and away from the pitch and he will be greatly missed. Everyone's thoughts are with Ugo's family at this difficult time."
First-team manager Mauricio Pochettino added: "Ugo was a lovely man and we had a very good relationship from the first day we arrived at the club. He was always a person who helped us a lot and we will miss him greatly.
"I send all my love to his family and friends at such a difficult time. It's a huge loss both personally and for all the Tottenham Hotspur family."
Spurs striker Harry Kane also paid tribute to his former coach, saying: "He was a big part of our development team at Spurs and a great character around the place, full of life, always laughing and joking, always in good spirits.
"He was a great coach and an inspiration to the younger players, he'd been there and done it at the very highest level and played for England. All our thoughts from myself and the players go out to his family and friend. It's a sad moment for everyone at the club."
Ehiogu, who made four appearances for England during his playing career, had been a coach at Tottenham since 2014.