Prince Andrew, 61, will also stop using the style His Royal Highness in an official capacity, a royal source said.
It comes as he faces a US civil action over sexual assault allegations - claims he has consistently denied.
A source close to the duke said he would "continue to defend himself" against the case brought in New York by Virginia Giuffre.
But the source insisted a judge's ruling on Wednesday that the civil action could proceed was "not a judgement on the merits of Ms Giuffre's allegations".