The 37-year-old has hosted a weekly Sunday morning programme on the station since 2018.
The move comes as the latest series of ITV dating show Love Island secured its biggest launch audience since 2019.
ITV has also announced there will be two series of the show in 2023 – a winter series in South Africa and a summer series in Majorca – with Whitmore likely to host both.
The Irish presenter, who started her career reading news bulletins for MTV in her home country, has hosted the show since 2020 after taking over from close friend and original presenter Caroline Flack.
She is married to Love Island narrator Iain Stirling and also hosts the spin-off interview show Aftersun.
Heidi Dawson, controller, BBC Radio 5 Live, said: “Laura has made the difficult decision to leave her weekend show after a brilliant four years.
“We’d like to thank her for the energy, insight and humour she has brought to this programme and look forward to working with her again in the near future.”
– BBC Radio 5 Live will launch a new Sunday morning show combining sport and current affairs discussion, which will lead into the afternoon of live football commentaries.