Dermot O'Leary, Gordon Ramsay, Gino D'Acampo, Phillip Schofield, Holly Willoughby, Jonathan Ross, Myleene Klass and Amanda Holden are among those supporting the five-year programme, which aims to improve the mental or physical health of some 10 million people.
Britain Get Talking, a riff on the flagship show's acronym, is also backed by mental health charities Mind and YoungMinds, and SAMH in Scotland.
Judges Simon Cowell, Amanda Holden, Alesha Dixon and David Walliams watched as a short video aired.
The clip saw backstage crew holding up cards that read: "Use our silence to talk to each other."
Donnelly said: "In the last 15 years there has been a staggering 48% rise in anxiety and depression among British children.
"But something as simple as talking together and listening to each other can build our mental wellness."
Ant McPartlin added: "We all know that these days there are more distractions than ever, because we are looking at the telly or we're looking at our phones.
"But, it's so important for our mental wellbeing to remember to get together with people we care about and talk."
After a pause Donnelly joked: "The hardest thing was keeping David Walliams quiet for a moment."
He added: "Seriously though, just taking time to talk with your nearest and dearest can really make a difference, especially for young people, so please make sure tonight is just the start."
Over the next month ITV will air advertisements featuring some of its best-known stars, who will use silence to encourage those at home to talk to one another.
ITV chief Carolyn McCall said: "At the heart of ITV's social purpose strategy is this new five-year commitment to help make mental wellness a priority in all our lives.
"We've worked with our long-term strategic partner, Mind, as well as YoungMinds to develop Britain Get Talking.
"The campaign highlights the importance of talking and listening in building mental wellness, ensuring we make looking after our mental health as much of a part of our daily lives and culture as our physical health."
Mind's chief executive Paul Farmer said: "We all have mental health, just as we all have physical health, and we can learn to look after it.
"At a time when only a third of people with a mental health problem get access to any kind of help and support, it's important to do whatever we can to help people take steps to stay well and try and prevent mental health problems developing in the first place.
More information can be found at www.itv.com/BritainGetTalking and www.stv.tv/BritainGetTalking.