In doing so they became the first French pair to win the year-ender since 2005 when Michael Llodra and Fabrice Santoro won the title in Shanghai.
Having begun the year by completing their Grand Slam collection at the Australian Open the French duo will hope to end it in triumphant fashion when they play at the Davis Cup Finals next week in Madrid.
Once the seventh-seeded French team broke for a 3-1 lead they were always in command against the South African/New Zealand pairing.
Mahut saved a break point at 2-3 in the second set before a Klaasen double fault to gift a break proved decisive.
They claimed the title without dropping a set and finished the season on an 18-set winning streak having also won the Paris Masters title this month.
"Thank you for sharing the court with me, for having so much enjoyable moments and giving me so much joy when I am with you on the court," said Herbert.
"You played an unbelievable final, so thank you for that."
(Reporting by Martyn Herman, editing by Pritha Sarkar)