The German's team-mate and title rival Lewis Hamilton won the race, meaning Rosberg had to finish third or better to claim overall glory, and he managed to hold off a stern challenge from Ferrari's Sebastian Vettel to claim second on the podium.
Hamilton led throughout the race, and he deliberately slowed the pace during the latter stages in an attempt to put pressure on Rosberg, despite strict instructions from his team to not play any strategic games.
Rosberg was unhappy with Hamilton's tactics during the Grand Prix, admitting that he did not enjoy the race, but he was ecstatic that he was able to hold on for overall glory.
"That was definitely not the most enjoyable race I've ever had," Rosberg said. "With Max at the beginning and then with those guys coming up at the end, really not very enjoyable those last laps. I'm glad it's over, and I am ecstatic. "
The 31-year-old has now replicated the achievement of his father Keke Rosberg, who claimed World Championship glory in 1982, and he admitted after the race that he was proud to follow in his father’s footsteps.
He added: "I am very proud to have done the same feat as my dad achieve."
Vettel joined the Mercedes duo on the podium in Abu Dhabi after claiming a third place finish in the race, while Red Bull duo Max Verstappen and Daniel Ricciardo were fourth and fifth respectively.
The rest of the top ten was made up of Ferrari’s Kimi Raikkonen, Force India duo Nico Hulkenberg and Sergio Perez, Williams’ Felipe Massa and Fernando Alonso of McLaren.