Hartley has been replaced at Toro Rosso after one full season in F1, having been handed a shock grand prix shot by Red Bull late last year after several years in sportscars.
The New Zealander, twice a World Endurance champion with Porsche and a Le Mans 24 Hours winner, scored four points for Toro Rosso.
Honda made significant progress in F1 this year in performance and reliability terms, which helped it secure Red Bull’s confidence to partner with the Japanese manufacturer for 2019.
“Everyone at Honda enjoyed working with Brendon throughout the year,” said Honda technical director Toyoharu Tanabe.
“He was very strong on the engineering side, always giving very precise and useful feedback, based on his great experience working with hybrid power units and as a double world champion and Le Mans winner in LMP1.
“That feedback accelerated our development in terms of set-up work, which helped us progress over the course of the year.
“Thank you Brendon, and we wish you all the very best for the future.”
Hartley was not mentioned in the team’s release confirming Alexander Albon as Daniil Kvyat’s 2019 teammate.
Toro Rosso did later share a team photo in a social media post with the message: “Thank you for your commitment this year, Brendon! All the best for the future!”
Though Hartley’s year was short of major results compared to teammate Pierre Gasly, he did qualify sixth for Honda’s home race in Japan.
Honda motorsport boss Masashi Yamamoto added: “On behalf of Honda, I would like to express my thanks to Brendon for all his hard work this year.
“Brendon is always a friendly and charming person who immediately embraced Japanese culture and Honda’s way.
“It gave everyone at Honda so much power and confidence in what we were doing this year after several difficult seasons.
“I particularly remember when he qualified sixth at our home race in Suzuka. That meant a lot to Honda.
“We will miss him and wish him all the best for the future.”
Brendon Hartley, Toro Rosso STR13
Photo by: Andy Hone / LAT Images