Top-seeded Alcaraz won 6–3, 6–2.
"I'm very happy to win this tournament, it's great to end these ten days like this," Alcaraz said after the win.
"Of course, the conditions today were very tough," he continues, but also notes that Medvedev did not play at his best level.
The 19-year-old Spanish tennis star - the youngest world number one on the men's side - captured his third ATP Masters 1000 title. He is the first men's player since Rafael Nadal to win Indian Wells without losing a set.
After the victory, Alcaraz is again ranked number one in the world, despite a late start to the year. An injury caused him to miss the Australian Open, where Serbian tennis star Novak Djokovic captured his 22nd Grand Slam title.
Rybakina's revenge
Kazakhstan's Yelena Rybakina won the classic WTA tournament Indian Wells, after defeating Belarusian Aryna Sabalenka 7–6, 6–4.
It was Rybakina's first career win against world number two Sabalenka. Rybakina, ranked number ten, last lost to Belarusian Sabalenka in the Australian Open final in January.
"It's actually the first time it's gone my way," Rybakina said as she accepted the trophy after the Indian Wells victory.