The Brit had previously appeared somewhat reserved in his support for Rosberg's championship win, but has now taken to social media to congratulate him.
"We said we'd be champions back then, now we both are!" said Hamilton. "Congratulations Nico, you did everything a champion needed to do. Well deserved"
Rosberg's championship win means that the two former-karting team mates will form one of just two world champion driver pairings on the 2017 grid with Ferrari's Kimi Raikkonen (2007) and Sebastian Vettel (2010-13) being the other.
Bahrain International Circuit - Winter testing