The 31-year-old's elevation is remarkable as it comes just five months after he slumped to 22 in the world - his lowest ranking for 12 years - when he was knocked out of the French Open in the quarter-finals.
Serbia's Djokovic, a 14-time Grand Slam victor and four-times a champion in Paris, will now replace Nadal as world number one when the new rankings are released on Monday (November 5).
The 16th seed knocked out France's home hope Richard Gasquet 6-3, 6-3.
The Swiss star missed the event the past two years due to a combination of injury and selective scheduling.
This December the Arabians set to organise a special exhibition match between tennis' two top-ranked players - Rafael Nadal and Novak Djokovic. I've practiced with the guys and felt, in terms of tennis, better than I thought one week ago.
Nadal's withdrawal also puts his participation at the ATP Tour Finals in London at doubt.
Svitolina fights off Bertens to reach Singapore final — WTA Finals
Bertens played too risky a brand of tennis , posting 41 winners to 12 for Svitolina, but also making 63 to 36 unforced errors. Bertens regrouped and was on the brink of levelling it up at 40-0 in the 10th game but cracked under the pressure.
Speaking after the victory, he said: 'I am very close to London, to securing my spot mathematically. "As long as I don't feel like I'm taking a chance on my health prior to London that's the key as well".
"It's been a hard year for me in terms of injuries, and so I'd prefer to avoid doing anything drastic", Nadal told the media minutes before his intended match against compatriot Fernando Verdasco. I'm happy practicing. I'm happy doing other things, and I didn't want to play there at that time. "So as I said, I can't be too ecstatic about it".
Saudi Arabia has faced criticism following the recent death of journalist Jamal Khashoggi, a critic of the Saudi government who was killed at the country's consulate in Istanbul in October.
Barty, who lost to Aryna Sabalenka on Tuesday, now has to wait for the outcome of Garcia and Sabalenka's match to see if she will progress to the semi-finals on Saturday.
The Serb will lead the ATP Rankings in men singles for the first time in two years, with Briton Andy Murray having taken the top honour from him in Paris in November 2016.