Laura will start her role when the show relaunches this September with a new-look set, title, title music and format.
She is currently the BBC political editor, and her last assignment in that post will be covering the local elections in May.
“I couldn’t be more delighted. For decades Sunday morning has been the moment to explore the events that shape us and to challenge and listen to our politicians,” Laura said.
“It’s an honour to take the chair for that conversation in the 2020s.”
Jonathan Munro said: “Laura’s the perfect host for our flagship weekend politics show – she’s an engaging presenter and a razor-sharp political interviewer, and she knows exactly which questions audiences want answered.”
The programme was previously The Andrew Marr Show, which Andrew Marr presented for 16 years before leaving the BBC at the end of 2021. Before that it was Breakfast with Frost, presented by David Frost.