Bowman, formerly a presenter on Radio 1, will leave her Saturday morning slot as US musician Morgan takes over the 10am programme on November 2.
She will continue to work with 6 Music after her show finishes.
The BBC said: "Edith Bowman's series will come to an end but she will continue to work with 6 Music with occasional specials planned for next year."
Fun Lovin' Criminals star Huey Morgan and Elbow frontman Guy Garvey also face schedule changes for their weekend shows.
Former Catatonia star Cerys Matthews - named music broadcaster of the year at this year's Sony Radio Academy Awards - is having her Sunday morning 10am show expanded from two to three hours.
She said: "I'm happy that I can now lay down what I think will be not only a Sunday morning show to wake up and ease the listeners into their day of rest, but take it right through to provide the perfect soundtrack to their Sunday lunch."
Garvey, who joined the station six years ago, moves from 10pm to 2pm with his Finest Hour Sunday show. He said: "I think what we do on the Finest Hour will work just as well on a lazy Sunday afternoon."
6 Music's head of programmes Paul Rodgers said the changes were "a further display of our commitment to showcase some of the most charismatic talent in music radio right now".
"It's great to bring Huey's New York attitude to Saturday mornings, which will be the perfect complement to Cerys' eclectic and absorbing music discoveries on a Sunday morning. Guy's exploration into music, hand in hand with his listeners, brings the perfect soundtrack to Sunday afternoons," he added.
Another change will see film-maker and DJ Don Letts's show brought forward from midnight to 10pm on a Sunday.