But complaints about BBC news presenter Peter Sissons's "insensitive" handling of the Queen Mother's death were rejected.
Moyles referred to Church's 16th birthday on his afternoon show in February this year.
He told listeners he wanted to "lead her through the forest of sexuality now that she had reached 16".
The comments were Moyles' style of humour and were not meant to be taken seriously, said the BBC.
But the Broadcasting Standards Commission (BSC) agreed with a listener who said the remarks were inappropriate.
It noted Moyles was known for his "near-the-knuckle" approach.
But it felt "the explicit sexual content and humour had exceeded acceptable boundaries for the time of transmission".
Moyles has been in trouble with the watchdog before.
He was found to have "exceeded acceptable boundaries" by making offensive comments about an actor's wife on his BBC Radio 1 show two years ago.
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In his previous job at Capital Radio the BSC upheld a complaint about his "aggressive and sexually suggestive" comments to a young female caller.
Sissons was criticised by viewers for an interview with the Queen Mother's niece, the Hon Margaret Rhodes, who had been present at the her bedside during her final moments.
Sixteen viewers complained but the BSC said the interview had been "conducted with due reverence and respect and would have been unlikely to have offended the majority of the audience".
The BSC upheld a complaint against BBC One's Newsround for an interview which appeared to encourage cannabis use, in January.
The BBC said it was clearly not the intention of the interviewee or the programme to condone drug taking, but the interviewee's comments were "open to misinterpretation".
This was spotted at the time, and at the end of the programme the audience was invited to make comments about the dangers of illegal drugs.