The Formula One world champions posted a video of Rosberg and Mercedes team boss Toto Wolff signing the new contract with the caption “It is done” on their official Twitter page.
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Rosberg, 31, has raced for Mercedes since 2010, finishing second in the drivers’ championship for each of the past two seasons.
Rosberg is understood to have pushed for a three-year deal with the team while Hamilton has already admitted he wants to see out his F1 career with the Silver Arrows.
Rosberg won the opening four races of the season but the momentum has since shifted Hamilton’s way.
But their relationship is a fractious one, punctuated by a number of on-track clashes. “I wished they’d saved their money”, Hamilton said, describing the circuit as “amazing” but lamenting its loss of character.
Formula One has clarified the rules on radio communication between teams and drivers in the wake of incidents that have cost competitors points this season.
“It’s come about because fans have said “we’re like puppets out there”, said Rosberg.
“The best approach for me to win races is just to focus on the weekend at hand, which is Hungary”.
“Today I missed a long run so when I get into the race will be the first time really attacking and making those tyres last as long as they need to go”.
He added: “I think the front-wing endplate might have been damaged, the sidepod wing maybe – not a lot of damage”. Though it is somewhat bright, the track remains damp following earlier showers, meaning we could see some initial running on Inters.
He trails Rosberg by just one point after cutting the lead from a cavernous 43 behind. However, his quick lap ended with an untidy slide through the final corner, which cost him time compared to the Red Bulls and his teammate Vettel.
McLaren changed Alonso’s power unit in between sessions after discovering what Honda claimed was “an anomaly in Fernando’s data during FP1”.
However, at T11, Hamilton got onto the grip-less concrete and spun his auto into the barrier, side on, registering 10.4G, meaning a trip to the medical centre was nonnegotiable.
The Red Bulls of Daniel Ricciardo and Max Verstappen were fifth and sixth, but both men chose not to use any of their supply of the super-soft tyres.
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Vettel, who has struggled for consistency with Ferrari and suffered successive gearbox problems, said: “I’m not entirely happy with the balance, but I think we can improve overnight”.
