The 28-year-old -- who will forever be remembered for the extraordinary goal he scored in Wales' Euro 2016 quarter-final win over Belgium -- only started five matches last season and made 30 appearances in all.
Robson-Kanu -- whose initial contract last year was a two-year deal with the option of a third year -- scored three times for the Baggies.
However, Robson-Kanu -- who will compete with Salomon Rondon and new signing Jay Rodriguez for the striker spots -- said he hadn't needed much convincing to sign the new deal.
"I'm delighted because it's an opportunity to build on the good work we did last season and now I'm just looking forward to the new one," Robson-Kanu told the club's website.
"It was an easy decision. I've enjoyed my time here playing under (manager) Tony Pulis. It was a strong season and I want to build on the good work and contribute to a more successful future."