The singer and TV presenter, 47, who found fame at the age of 12 with his top five Christmas hit Walking In The Air, was not on air while the BBC investigated complaints about him.
A statement from his spokesman said that Jones "has given his assurance" that his past behaviour "will never be repeated".
The spokesman said: "About three months ago Aled voluntarily agreed to step away from his presenting commitments whilst the organisation conducted a review.
"Aled was devastated to learn that some of his past behaviour outside the BBC had caused distress to others.
"He deeply regrets this behaviour and is very sorry for the hurt it has caused. Aled has given his assurance that it will never be repeated.
"Aled will now continue with his roles at the BBC. There will be no further comment."
A BBC spokesman said: "As Aled has previously confirmed, over recent weeks the BBC has been considering complaints about his past behaviour. During this period, Aled has not been presenting on the BBC.
"While the behaviour under review was not related to his work with the BBC, Aled recognises it was inappropriate and caused real distress to others.
"He has apologised for this and assured the BBC that there will be no repeat of this behaviour in future.
"We can confirm that Aled Jones will be resuming his radio and television presenting roles with the BBC over the coming weeks."
The former choirboy received an MBE in 2013 for his services to music and broadcasting.
He became a national radio presenter after signing up with Classic FM in 2002 and went on to present a Sunday morning show for BBC Radio 2.
Jones, a father of two, was a contestant on Strictly Come Dancing in 2004 and further TV work has included Daybreak, Escape To The Country and Cash In The Attic.
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