The BBC said Raworth, 53, will present the temporarily-titled Sunday Morning programme from January 9.
The news follows Marr’s recent announcement that he is leaving the BBC after more than two decades.
The BBC said in a statement that Raworth will front the popular show for a “short period” while a recruitment process for a permanent presenter takes place.
Once a permanent appointment is made, the programme will relaunch with a new presenter, title and a new look, the BBC said.
Raworth has covered for Marr in the past and is one of the main presenters of the BBC News At Six and Ten, which she has worked on since 2003.
She joined the BBC regional trainee scheme in 1992 and went on to report for Greater Manchester Radio, and later moved to Brussels as a BBC Regions correspondent.
In 1995, she moved to Leeds for BBC Look North, which is where she first presented the news. She joined BBC Breakfast News in 1997 as a co-presenter.
Raworth has also presented for the broadcaster from the Oscars in Los Angeles, in Washington for Bill Clinton’s impeachment trial, and during a special programme for the Queen’s Golden Jubilee celebrations in 2002.
She hosted BBC Breakfast alongside Jeremy Bowen from its launch in 2000 and has also presented election night coverage, Watchdog, Crimewatch and the Chelsea Flower Show.
Marr’s last show will air on December 19.