Thompson, who has been at the Japanese car marque for 13 years, is to step down at the end of next month. He is understood to have secured a senior marketing role outside the automotive industry, which he will take up later in the year.
It is not known who will replace Thompson at Honda; a spokesman said the job would initially be advertised internally.
Thompson joined Honda in 1993 and has worked in a number of roles across its three divisions: cars, motorcycles and power equipment.
After taking over from Chris Brown as head of marketing in 2002, Thompson oversaw 2003's "cog" campaign for the Accord model, created by Wieden & Kennedy. He has handled several Honda campaigns since, including the current high-profile "impossible dream" advertising.
Thompson was unavailable for comment.
Separately, a Honda Civic campaign, which breaks this Friday, will enable consumers to download the TV ad as a videocast.
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