The LA Galaxy star, who spent much of his career at Manchester United, told ShortList that manager Arsene Wenger swayed his middle son.
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"I tried to get Man United shirts on them early," Beckham said.
"Two of them are Man United fans and one of them's an Arsenal fan. I don't know how that happened, but my middle son, Romeo, is an Arsenal fan."
He added: "Actually, I do know how it happened. I took him to an Arsenal game and Arsene Wenger treated him so well, gave him a shirt with his name on the back and his favourite number.
"I had that when I was a kid with Man United. I let them support whoever they want. They don't have to support the teams I played for."
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Beckham kept fit by training with the Arsenal squad for a spell in January 2008.
Last year, Beckham's former club AC Milan beat Arsenal 4-3 on aggregate in the Champions League last 16.
"When I found out that my son, Romeo, supports Arsenal, I became disappointed," the midfielder said before the tie.
"I can't bring myself to support Arsenal, although I do respect the club. I am convinced that Milan will go through."
