The broadcaster's TV coverage of the second race of the season, the Australian Grand Prix on Sunday, achieved a peak audience of 3.4 million viewers.
Tina Shortle, marketing director at swiftcover.com, said:
"This sponsorship deal forms part of our integrated marketing strategy to build on the swiftcover.com brand and reach our target audience in an unexpected and impactful way. In a highly competitive market, it is key that our brand name gets on people's shopping lists and encourages them to get a quote."
The creative will feature frustrated Formula 1 drivers talking to chickens wearing headsets in the pits of a race track, mirroring the "call centre chickens" featured in the swiftcover.com TV advertising.
Last year's F1 season on ITV was sponsored by LG Electronics.