Ehiogu collapsed at Tottenham's training centre, where he worked as the club's under-23 coach, on Thursday after suffering a cardiac arrest and his death was announced on Friday morning.
Southgate had a close bond with Ehiogu, having shared defensive duties with him at Aston Villa, Middlesbrough and England and the pair won two League Cups together in 1996 and 2004.
A shocked Southgate offered fulsome praise for Ehiogu's personal and professional qualities in a statement released by the Football Association.
"I'm stunned and deeply saddened by Ugo's passing and clearly my initial thoughts are with his wife Gemma, his children and his family," he said.
"I know that football will be grieving because he was so highly respected by everybody he worked with and losing him at such a young age is difficult to come to terms with.
"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 him.
"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. It felt like a true partnership with Ugo because we were prepared to put our bodies on the line for each other.
"We shared highs, lows and won a couple of trophies together with Villa and Boro and it's those memories that I will always cherish when I think of Ugo.
"He was one of the most professional people I played with in terms of how he applied himself to his job and it was great to see him progressing through the coaching pathway with that thirst for learning.
"I've spoken to several of our former team-mates today and there's just a sense of disbelief that we're having these conversations.
"Ugo was a credit to football, a credit to his family and he will be missed by everybody who was lucky enough to know him."
Another of Ehiogu's Villa colleagues, Paul Merson, was unable to finish his own on-air eulogy as emotion got the better of him.
Speaking on Sky Sports as footage of his friend played, former Arsenal favourite Merson said: "Billy Joel sings that song, 'Only the good die young' and that is him.
"He was a top player, a top bloke and a good friend as well. I talked to him recently and he was always winding me up, telling me Tottenham had some good players coming through..."
Merson was unable to fight away the tears and his tribute was cut short.
Ehiogu began his career as a trainee at West Brom before he was taken to Villa by Ron Atkinson in 1991. He went on to feature in more than 300 matches for the midlands club and played in their FA Cup final defeat against Chelsea in 2000.
Ehiogu joined Middlesbrough for a then club-record £8million fee later that year, and in 2001 he scored his only goal for England in Sven-Goran Eriksson's first game in charge, a 3-0 friendly victory against Spain.
He won four caps in total, all friendlies, a tally that would surely have been higher had it not been for the rare defensive strength England enjoyed throughout his prime.
Tottenham thanked North Middlesex University Hospital, Royal Brompton Hospital and Harefield Hospital for their efforts treating Ehiogu and 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."
Their FA Cup semi-final against Chelsea on Saturday will see both teams wearing black armbands and holding a minute's applause, with Villa's derby against Birmingham following suit.
Boro owner Steve Gibson, on behalf of the Teessiders, said: "He wasn't just a good footballer, he was a great man. It's so sudden and so shocking, my deepest sympathies go to his family and all who knew him.
"Ugo and Gareth Southgate were the rock on which Steve McClaren brought the club its best period in its history. All of Middlesbrough Football Club will miss him."
McClaren, former Boro boss, added: "He was a gentle giant of a man off the field but a real warrior on it."
Knee injuries plagued the final years of Ehiogu's playing career, but he had spells with Leeds, Rangers and Sheffield United before he retired from football in 2009.
He tried his hand at broadcasting and in the music industry, helping set up the record label 'Dirty Hit', but settled on coaching, a pathway he was tipped to excel in.
The humanity those close to him spoke so readily of was in evidence in the final tweet from his account, a post which read: "Gave a homeless girl £10 last night in Dalston," he wrote on March 29. "She didn't ask or beg. Random impulsive act from me. Not gonna lie, felt good. £dosomethingkind."
Additional reporting by the Press Association.