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Medvedev came into the decider with 19 straight ATP Tour wins but Alcaraz made light work of the Russian, winning 6-3 6-2 in 72 minutes.
Alcaraz's triumph is his third Masters title from three finals, not dropping a set in any.
🏆🏆🏆
— ATP Tour (@atptour) March 20, 2023
🫴🫴🫴@carlosalcaraz joins his countryman Rafael Nadal as the only players to win at least three ATP Masters 1000 titles as teenagers 💫@BNPPARIBASOPEN | #TennisParadise pic.twitter.com/1UB0HU75Gl
It also ensured he returns to the rankings' summit – supplanting 2023 Australian Open champion Novak Djokovic, who did not participate at Indian Wells.
Alcaraz, the 2022 US Open champion, has won two of three events since returning after three months out with abdominal and hamstring injuries that forced him to miss the opening slam of the year.
The Spaniard had labelled Medvedev the "best player right now" in the lead-up to the match but was on top immediately, opening up a 3-0 lead as he hit 10 winners to the Russian's two in the first set.
His dominance continued, winning the first 10 points of the second set, taking a 4-0 lead before prevailing with his second match point.
NUMERO UNO 🇪🇸🏆
— ATP Tour (@atptour) March 20, 2023
The moment @carlosalcaraz won his third ATP Masters 1000 title without dropping a set! @BNPPARIBASOPEN | #TennisParadise pic.twitter.com/BjqnLHVf2I
Alcaraz finished with a 19-4 advantage in winners while Medvedev did not manage one ace for the match, marking the first time that has occurred since February 2020 against Gilles Simon in Marseille.
"It has been a really amazing run here, such an amazing experience," Alcaraz said.
When asked if he had played a near perfect match, Alcaraz told Amazon Prime: "Yes, probably. I played really, really well.
"I made no tactical mistakes, which is really important against Daniil. I would say I was perfect in that way.
"I'm really happy with the way I played, the trophy and of course to be world number one."
While Alcaraz will return to the top of the world on Monday, compatriot and idol Rafael Nadal is set to drop out of the top 10 for the first time since April 2005.
Medvedev had won in Rotterdam, Doha and Dubai recently and was gunning to be the first man to win four titles in five weeks since Andy Murray in 2016, but he was completely outclassed by his 19-year-old opponent.
The Russian had to overcome several hurdles to reach the final, having rolled his ankle in his fourth-round win over Alexander Zverev while he also hurt his thumb in a quarter-final defeat of Alejandro Davidovich Fokina.
Yet despite the trials and tribulations, and his humbling loss in the final, Medvedev was in good spirits.
"I had a pretty toxic relationship here with the courts, a love-hate relationship," he said. "So I'd like to thank the court!
"I only played on this court. I gave it a hard time so it gave me a hard time also. Rolled the ankle, the thumb... but it gave me the chance to finish the tournament.
"Thanks a lot to this court, I'll definitely be back.
"I really love this tournament, I'll be happy to come back many more years to come and hopefully I can start to love this court and Indian Wells together."
Addressing the crowd, Medvedev quipped: "Sorry I didn't make this final entertaining. I tried, I don't like to lose, but today was unfortunately pretty easy.
"I hope you still enjoyed it."
