Southgate had a six-year spell at Villa, winning the League Cup and becoming club captain.
Asked about Ellis' death, Southgate said: "It's very sad.
"He had a good innings, at 94.
"He was a brilliant chairman from a player's perspective – slightly harder work for some managers, but brilliant as a player.
"The day I signed he took me to dinner with Brian Little, then I stayed at his house rather than travel back to London.
"He made me welcome from the start."
Southgate resigned the captaincy because he wanted to leave Villa to fulfil his playing ambitions, and joined Middlesbrough in 2001.
Some Villa fans claimed Ellis' refusal to spend more money hindered the club's development – although more recent, serious financial issues have put those complaints in some perspective.
Southgate said: "He was genuinely passionate about the club.
"If you look at his time as chairman, not only were we always competitive in the top six, we owned our own training ground and ground.
"The club had no debt when he sold it.
"He was a fantastic custodian of the club."
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