Cotton announced on Wednesday (August 8) that she is expecting her first child with partner Jesse Wood.
Former breakfast show presenter Cox will fill in for Cotton's 10am-12.45pm show later this year.
The official Radio 1 Twitter feed announced: "We have news! We can confirm that the wonderful @sarajcox will be filling in for Fearne when she goes on maternity!"
Cox retweeted the post, adding the hashtag: "#sooochuffed".
Radio 1 have yet to make an official announcement as to when Cotton will be starting her maternity leave.
Cox stated last year that she would be interested in working on The X Factor or The Xtra Factor.
Chris Moyles will host his final ever breakfast show on BBC Radio 1 on Friday September 14, ahead of Nick Grimshaw's first breakfast show for the station on September 24.