Ehiogu, who worked as Tottenham's U-23 coach, collapsed at the North London club's training ground on Thursday.
He died in the early hours of Friday, the Premier League title contender said in a statement.
"Words cannot express the shock and sadness that we all feel at the Club," said Tottenham's head of coaching and development John McDermott. "Ugo's immense presence will be irreplaceable."
Ehiogu, who started out as a trainee at West Bromwich Albion but spent most of his career at Aston Villa, was capped four times by England.
He would doubtless have won more caps but for injury and competition from younger defenders like Rio Ferdinand and John Terry.
As well as playing more than 200 times in nine years for Villa, London-born Ehiogu played 126 games for Middlesbrough after becoming their then-record signing for 8m pounds ($10.24m) in 2000.
He won the League Cup with both Villa and Middlesbrough.
Also playing for Rangers in the Scottish Premier League, Ehiogu scored a winner against Celtic in the 2007 Old Firm derby with a spectacular overhead kick that was later voted the club's goal of the season by fans.
He ended his professional career at Sheffield United in 2009 and joined Tottenham's coaching staff in 2014 after a spell with the England U-20 side.
Championship side Villa said they would be holding a minute's applause before their home derby with Birmingham City on Sunday with both sets of players wearing black armbands as a mark of respect.
Tottenham cancelled academy matches scheduled for the weekend and postponed Monday's U-23 game at Manchester United.
Shocked former team mates, managers and playing rivals paid tribute while the League Managers' Association mourned "one of the country’s brightest young coaches".
"As a player and then a coach, Ugo was a credit to the modern game," said LMA chairman Howard Wilkinson.
"To think this could happen to a man of his fitness and age. It is devastating, crazy," former Villa team mate Lee Hendrie told Sky Sports television.
"Ugo was one of our heroes at Cardiff when the club won its only ever major trophy," said Middlesbrough chairman Steve Gibson. "Ugo and Gareth Southgate were the rock on which Steve McClaren brought the club its best period in its history.
"He wasn’t just a good footballer, he was a great man."