The pair took over as the Friday presenters of the ITV daytime show in January 2021 and have since been dogged by claims they do not get on with one another off-screen.
But co-host Gibson told New! magazine: "Those two are like brother and sister! I don't know what's been written but they really do get on. Dermot worships Alison and Alison loves Dermot.
"She bought him a lovely watch not long ago, and they go round to each other's houses for dinner.
"You don't buy people watches and go round to their house if you don't like them, do you?"
Gibson, 37, made her debut guest hosting the show in November 2021, after she was drafted in at the last minute to replace Willoughby when she fell ill.
The TV presenter and former Big Brother winner is a regular contributor on This Morning but had never hosted before when she was asked to join Schofield on the sofa just a few hours before the show went live on air.
She has since stepped in regularly and has proved popular with viewers.
Gibson admitted it is hard for the This Morning presenters to find time to socialise off screen as they all have busy schedules.
She said: "We're all so busy. We all message each other but it's so busy being at This Morning, and being a working mum, it's difficult to pin everybody down.
"But, luckily, we do get to see each other at work."
Last year single-mother Gibson her three-year-old son Reggie-James even spent Christmas Day with Hammond.
She said: "Never had a Christmas dinner like it. Best Christmas dinner ever."
Gibson found fame after starring in Big Brother in 2010 and went on to win the reality show.
Watch: Alison Hammond and Dermot O'Leary presenting This Morning together