James Torbett, 51, of Lenzie, near Glasgow, was found guilty at Glasgow Sheriff Court on three charges of shameless and indecent conduct.
He sexually abused Mr Brazil, now 39, David Gordon, 38, and James McGrory, 44, between October 1967 and March 1974.
The jury took seven hours to reach their verdict and sentence was deferred until 27 November.
Sheriff Margaret Gimblett said: "It gives me great sorrow for someone who has done so much good in the past to deal with you."
She said that although Torbett was allowed to remain free at this stage, she would be looking over social inquiry reports and community service assessments.
Ms Gimblett also said: "During this time you will be allowed to remain in the community but do not assume when you come back that you will be allowed to do so."
Former Scotland star Mr Brazil told the trial last week that he was 13 when he was touched by Torbett after being invited back to Torbett's flat in Glasgow.
After the incident, he avoided socialising with Mr Torbett. He said he had always wondered if this had affected Celtic's decision not to sign him when he was old enough.
Mr Brazil was capped 13 times for his country and played for Ipswich Town, Manchester United, and Tottenham Hotspur.
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