The former Citybeat and Q Radio presenter will make his debut on the station on 23 September in the slot vacated by the veteran broadcaster.
The BBC said Mr Clements was a “great broadcasting talent” and a “great addition” to the station.
Mr Coyle’s programme, which ran between 10:30 and 12:00 on weekdays, was axed by the BBC last month.
This was despite the fact that it was the third highest rating show on Radio Ulster.
The new programme – The Stephen Clements Show – will fill that slot and will feature music and chat with listeners, according to BBC Northern Ireland.
Mr Clements, from Carrickfergus, Co Antrim, said he was “absolutely thrilled to be given this opportunity” at the BBC.
“It has always been my dream to broadcast on the most respected, most creative media platform on the planet,” he added.
“I am looking forward to sharing some fun and lots of laughs with the amazing people of Northern Ireland.”BBC NI said the move was part of its commitment to “refresh the station’s output” to engage and entertain audiences and to broaden the station’s appeal.
The BBC announced last Saturday that Mr Coyle would present a new daily programme on BBC Radio Foyle until spring 2020.