The supermarket said it wanted to make it easier for parents to encourage their children to eat healthily and would be promoting the range with offers including bags of apples and three-packs of prepared fruit for £1 each.
Scheving's character Sportacus, who calls fruit "sports candy", has been credited with reducing obesity in his home country of Iceland.
"The link-up gives us the perfect partnership," said Asda marketing director Katherine Patterson. "We want to help children lead healthier lives."
Asda is promoting the partnership by playing the Lazy Town theme tune in the foyer of Asda stores this weekend and at times during the summer holidays. This weekend children will be able to sample fruit in store and take part in competitions to dress up as Sportacus and his sidekick Stephanie.
Scheving's association with Asda follows a sustained campaign by the former European aerobics champion to get UK supermarkets and theatres to promote fruit and veg rather than sweets and confectionery.
In a shopper survey for Asda's parent company Wal-Mart, customers said they would buy fruit and veg if Sportacus's image was promoting it, Scheving claimed.
Patterson said Asda was also developing its Great Stuff range, and was considering launching cheese sticks, wraps and sandwiches, plus products suitable for children's dinners, within 12 months.