Her post on Sunday went on to thank the “brilliant medical teams who took such great care of me” and “the thousands of people who sent me such beautiful and encouraging messages”.
“Most of all [thank you] to my family: my two astounding kids and especially my husband Graeme, who was absolutely extraordinary throughout,” she said.
“It’s been a difficult time but one that has taught me so much about what really matters.
“I can’t say I suddenly regretted never having hiked the Inca Trail, more that I now see more beauty in ordinary things than I could have imagined.”
Her post also included a picture of her wearing a jumper bearing the words: “Life is beautiful”.
She said in August her cancer had been discovered “unexpectedly during a screening test” and urged anyone who was “avoiding a test or putting off an appointment” to get checked.
Laverne began filling in for Kirsty Young on Desert Island Discs in 2018, later taking over as permanent host.
The role has seen her interview the likes of Cillian Murphy, Steven Spielberg, Rebel Wilson, Delia Smith, Kate Mosse and John Legend.
She has previously presented BBC Two’s The Culture Show and Channel 4’s 10 O’Clock Live, and in the 1990s was a singer and guitarist with alternative rock band Kenickie.
A BBC spokesperson said: “We’re delighted to welcome Lauren back to the studio this month for The One Show and Desert Island Discs, with new episodes airing on Radio 4 from 1 December, and we look forward to welcoming Lauren back to BBC Radio 6 Music in the new year.”