Scott Mills was investigated over allegations of "serious sexual offences" against a boy who was aged under 16.
The BBC gave few details about his sacking on Monday, only that Mills had been dismissed due to claims over his personal conduct.
The Metropolitan Police said on Tuesday it had launched an investigation in December 2016 "following a referral from another police force" relating to "allegations of serious sexual offences against a teenage boy".
The alleged offences are said to have taken place between 1997 and 2000.
"As part of these enquiries, a man who was in his 40s at the time of the interview, was questioned by police under caution in July 2018," the Met added.
It said the Crown Prosecution Service ultimately decided "the evidential threshold had not been met to bring charges" and the case was closed in May 2019.
The police investigation into the allegations were first reported by The Mirror.
Mills, who has not yet commented on his sacking, was taken off air by the BBC last Tuesday.
The 53-year-old signed off that show saying "back tomorrow" - but Gary Davies presented Wednesday's show.
Mills took over from Zoe Ball on Radio 2's breakfast show in 2025 after a long career at the BBC and regional radio.
He was paid between £355,000 and £359,999.
His sacking is the latest in a series of controversies to befall the BBC in recent years and comes a week after it announced Matt Brittin would be its new director-general in May.
In an internal email on Monday, Lorna Clarke, the BBC's director of music, wrote: "I know that this news will be sudden and unexpected and therefore must come as a shock.
"Not least as so many of us have worked with Scott over a great many years, across a broad range of our programmes on R1, 5Live, R2 and TV.
"I felt it was important to share this news with you at the earliest opportunity.
"Of course, it will also come as a shock to our audience and loyal breakfast show listeners too.
"I will update everyone with more information on plans for the show when I'm able to. While I appreciate many of you will have questions, I hope you can understand that I am not going to be saying anything further now."
(c) Sky News 2026: Scott Mills was investigated over allegations of 'serious sexual offences' against boy under 16
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