Consumers can upload content via sainsbury's Feed Your Family website.
The content will feature in a series of ads by AMV BBDO that will run from Monday (30 May) to the final programme on Saturday 4 June, in a placement negotiated by PHD with ITV.
Sainsbury's 'Feed Your Family for £50' menu was launched earlier this month, backed by a £10m campaign.
It has been designed for families who wish to keep to a budget with menus containing the recommended daily five portions of fruit and vegetables, and has been approved by the British Nutrition Foundation.
Claire Harrison Church, Sainsbury's director of brand communications, said: "The 'Feed Your Family for £50' initiative is proving to be really popular with our customers and over 400,000 people have already visited our website to learn how they can make healthy, nutritious and tasty meals on a budget.
"Britain's Got Talent is a great show for all of the family to enjoy, so it provides a perfect platform to for us to thank customers for taking part, share their enjoyment with the country, and make them stars of the small screen."
David Wilding, PHD's head of planning, said: "The way in which the finals week is scheduled provides a real sense of momentum and excitement across the country. People can be watching the ad break in Britain’s Got Talent one night and starring in it the next.
"We hope that this idea will allow people to enjoy two much-talked-about things together over one remarkable week."
Community engagement work has been created by digital agency Dare.