Ehiogu, who worked as under 23-coach for Premier League title contenders Tottenham Hotspur, collapsed at the North London club's training ground on Thursday and was rushed to hospital.
He died early on Friday of a cardiac arrest, aged 44.
"Losing him at such a young age is difficult to come to terms with," said Southgate, who played alongside Ehiogu at Villa and Middlesbrough for almost 10 years and was also with him in the England squad.
"Most importantly, he was a gentleman and he is one of those characters that people would find it difficult to have anything bad to say about.
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"I probably played more games with Ugo than anybody else in my career and, while in many ways he was a gentle giant away from football, he was a colossus on the pitch," added the England manager.
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 8 million pounds in 2000.
He won the League Cup with both clubs.
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 under-20 side.
Championship club Villa said they would be holding a minute's applause before their home derby against Birmingham City on Sunday with both sets of players wearing black armbands as a mark of respect.
Tottenham, who are playing league leaders Chelsea in an FA Cup semi-final at Wembley on Saturday, will do likewise.
The club also cancelled academy matches scheduled for the weekend and postponed Monday's under-23 game at Manchester United.
"He was a person who always helped us a lot and we will miss him greatly. We are all in shock, it happened so quickly," manager Mauricio Pochettino told the club website.
"It’s a huge loss both personally and for all the Tottenham Hotspur family."
Middlesbrough chairman Steve Gibson said Ehiogu was one of the rocks in the team in the most successful period in the club's history.
"He wasn’t just a good footballer, he was a great man," Gibson said.
(Editing by Ed Osmond)
