The four-time world champion, who retired at the end of the 2022 season, had previously been linked with a comeback.
Vettel explained that F1 is "finished" for him, believing it is time for younger drivers to take over.
He had a distinguished career, winning 53 races and securing 122 podium finishes across 16 seasons.
However, Vettel did not rule out competing in other motorsport series, such as the World Endurance Championship and the prestigious 24 Hours of Le Mans event.