Both are newly created accounts, a spokeswoman for Bupa said.
Third City, which has clients including Wellcome Trust and Confused.com, has been tasked with handling consumer PR for Bupa's private medical insurance and workplace health offerings.
Chris Blackwood, partner at Third City, said the agency would help Bupa tell its "pioneering" story to businesses and members of the public.
Seymour PR, which was established in 2012 by Carie Barkhuizen, will handle consumer PR for Bupa's everyday health services.
This will include press office duties and campaigns to raise awareness of the healthcare company's dental surgeries, GP clinics and physiotherapy services.
Barkhuizen said: "Consumer awareness of health issues has never been more pronounced, and working with such an influential brand helps demonstrate our credentials in the sector. To transfer the #ForLiving sentiment from 'paid' to 'earned', we've kept our focus firmly on what everyday health means to consumers."
Bupa unveiled its 'For Living' brand slogan earlier this year, which is designed to help people get the most out of everyday life, Bupa UK brand communications manager Cheryl Rosenthal said in March.
The Bupa spokeswoman told PRWeek the agencies would handle separate briefs, but may integrate on certain projects alongside Bupa's existing UK PR agencies.
Bupa also works with FTI Consulting, which handles financial comms for the company.