Holmes, who hosts This Morning on Fridays, is said to have been unhappy with Jon Culshaw's impression of him that included jokes about his weight, such as the catchphrase: "I was fierce hungry, so I was."
A source told the News of the World: "Staff were surprised because initially Eamonn seemed to find the funny side. He has spoken about having no willpower to diet and being overweight, so it didn't seem a big deal."
The source added that Holmes's character will not feature in the new series of the show, but claimed that this was not linked to the complaint.
A spokesman for Holmes said: "There have been discussions with the BBC and Eamonn is happy to say the matter has been resolved."