Speaking on her final instalment of Woman’s Hour, Garvey said: “Genuinely, this has been one of the toughest decisions of my life.”
Starting next Spring, Garvey will host a new interview programme on BBC Radio 4, with further details forthcoming.
The presenter departs the series three months after her co-host, Dame Jenni Murray, also left the series she had hosted for over three decades.
She added: “Woman’s Hour is not just a radio programme, it’s one of the radio programmes, and I’ve had the chance to do it, and it’s just been an amazing privilege.