The German has never been world number one before, but he will take over the top spot next week when the rankings are updated.
He will also become the first German to finish a year as world number one in tennis.
After Alcaraz’s exit against Zizou Bergs, ranked 39th, the Spanish star can no longer overtake Zverev.
Alcaraz has been in great form since returning last fall after a long injury layoff.
Jannik Sinner has topped the rankings since April, but the Italian is currently suffering from a knee injury and will miss the rest of the season.
Zverev plays Kazakhstan’s Alexander Bublik in the round of 16 on Tuesday.