David Letterman thanked his fans for giving him "everything" in his final 'Late Show'

Speaking to his fans, he said: "Have you thought about a complete psychological work-up? The people who watch this show, there's nothing I can do to ever repay you. Thank you for everything. You've given me everything."

During the 80-minute broadcast, viewers were treated to celebrity guests, video montages and famous sketches, as well as a performance of 'Everlong' by the host's favourite band Foo Fighters.

The rockers previously performed the track on the show back in 2000 when David returned to the show after undergoing quintuple-bypass heart surgery, describing them at the time as "my favourite band playing my favourite song."

Meanwhile, celebrity fans took to the internet to send their well-wishes to the much-loved TV personality, with Kim Kardashian West saying the veteran broadcaster would be "greatly missed".

She wrote on Twitter: "Thank you for so many laughs! You will be greatly missed @Letterman (sic)."

Lena Dunham also praised David by saying he made her feel "like a trillion bucks" when she was interviewed on the programme.

Sharing a photo of the pair on Instagram, she wrote: "Dear Dave- you really know how to make a gal feel like a trillion bucks. Thank you for it all. Love- Lena (sic)."

Joking about the praise he received during the final show, David - whose slot will be taken up by comedian Stephen Colbert - urged fans to tone down the commendations because he hasn't died yet.

He quipped: "Do me a favour. Save a little for my funeral."