The sponsorship will start from Sunday 1 September and will run until January in a deal brokered by Bristol-based Creation Media.
Arron Banks, the chief executive of GoSkippy, said: "We're looking to reach our target market as quickly and effectively as we can.
"What better way to get our message – competitively priced cover and excellent service from a team of industry experts – to UK motorists over the airwaves, than TalkSport with a traffic and travel sponsorship?"
The insurance brand uses the character of bush kangaroo Skippy to represent the brand's values, which Banks describes as "service, humour and saving ordinary folk".
Adam Mills, the sales director of TalkSport, said: "Over a third of TalkSport's listeners tune in to the station while in their car, so sponsoring the traffic and travel updates is a perfect way to reach them."
Admiral previously sponsored the travel and traffic updates, in a deal which ended this summer.