The couple, who married in June 2010, were joined by guests including Matt LeBlanc, Thandie Newton and Oliver Parker at the ceremony.
Speaking at the launch of his new ITV2 fly-on-the-wall series Peter Andre: My Life, the singer admitted that he had kept the gig secret for most of the year.
"I did do a private gig very recently, no-one knew about it, for a very, very well-known person," he said, confessing that throat problems had left him unsure if he would be able to see the engagement through.
"I got there and I said to Claire [Powell, my manager] 'I don't know what I'm going to do'. So I basically talked," he said. "I actually have to be honest, I talked through his wedding. I was a bit scared. I thought I'd rather not do it, so I sung the verses."
Describing the Ross Geller star as a "really nice man", Andre said that the opportunity had come about "by chance".
"I did a couple [of songs], but the one that his wife danced to was 'Mysterious Girl'," he said. The 38-year-old added: "They're really nice people."
Peter Andre: My Life begins Wednesday at 9pm on ITV2.
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Watch Peter Andre's 'Mysterious Girl' video below: