The trio will share presenting duties for the Radio 4 panel show after the death of former chair Humphrey Lyttelton last year.
Brydon said: "[It's] not really a question of filling Humph's shoes because that couldn't be done - he was a complete one-off.
"I'm a real latecomer to it, I only came to it about three years ago but I'm so proud to be a small part of it and this is really just about continuing that lovely atmosphere."
He added: "People don't do it for the money, they do it for the enjoyment of it and it's a unique radio show and one that I think we're all hugely proud of."
Regular panellist Barry Cryer insisted that the show's return is no disrespect to Lyttelton and that his would be "big shoes to fill", but added that a "torrent" of emails had called for the programme to continue.