The United Kingdom's Metropolitan Police said the boy at the centre of the investigation, first reported by the Mirror newspaper, was under the age of 16.
The investigation began in 2016 following a referral from another police force and examined alleged offences reported to have taken place between 1997 and 2000.
"The investigation related to allegations of serious sexual offences against a teenage boy," the force said in a statement, without disclosing his age.
Police said a man in his 40s was questioned under caution in July 2018 and that a full file was passed to the Crown Prosecution Service.
Prosecutors concluded there was insufficient evidence to bring charges, and the investigation was closed in May 2019.
The BBC said it does not comment on matters relating to individuals but confirmed Mills was "no longer contracted" to work for the corporation.
It has not said whether the police investigation played any role in the decision.
Mills did not immediately respond to a request for comment.
Mills, 53, took over Radio 2's flagship breakfast show in January 2025 from Zoe Ball, one of the corporation's highest-paid presenters at the time.
His departure is another blow for the BBC, which is still dealing with the fallout from former news presenter Huw Edwards' 2024 conviction for making indecent images of children.
