Ehiogu, who was the club's under-23s coach, collapsed at Spurs' training centre yesterday after suffering a cardiac arrest.
He received immediate treatment before being transferred to hospital, where he passed away in the early hours of this morning.
Tottenham announced his death at 9am, saying in a statement: "It is with immense sadness that we announce the passing of Ugo Ehiogu."
Ehiogu, who played for Aston Villa and Middlesbrough and was capped by England on four occasions, joined Spurs as a coach in 2014.
Spurs' head of coaching and player development John McDermott, said: "Words cannot express the sadness that we all feel at the club. Ugo's immense presence will be irreplaceable.