The young phenomenon will now face a battle of the generations against seven-time champion Novak Djokovic (36), who earlier on Centre Court eased past Italian Jannik Sinner (21) to reach his 35th Grand Slam final.
For seven games under the roof this felt like it could be a contest as third seed Medvedev, who like Alcaraz was contesting his first Wimbledon semi-final, kept pace with the top seed.
But from the moment Alcaraz broke the Medvedev serve for a 5-3 lead in the opening set it felt as though he had the grandest stage in tennis to himself with a virtuoso display.
At times it looked as though Alcaraz was toying with his opponent, working through his extensive arsenal of weapons to dismantle the Russian in merciless fashion.
Two nonchalant service breaks sealed the second set and the Spaniard accelerated towards victory with another one early in the third set as Medvedev's shoulders slumped.
Like a lion toying with its prey, Alcaraz offered back a couple of service breaks with some over-casual tennis but the respite was brief and an out-classed Medvedev was put out of his misery in one hour and 50 minutes.
Alcaraz is the third Spaniard to reach the Wimbledon men's singles final after Manuel Santana and Rafa Nadal and the fourth youngest in the professional era.
Djokovic, who overwhelmed Alcaraz in the French Open semi-finals last month, is bidding to become the oldest men's singles champion and match Margaret Court's all-time record of 24 Grand Slams.
The Serbian has not lost on Centre Court for 10 years, but Alcaraz said he is ready for the challenge.
"Everybody knows it's going to be really difficult but I will fight, I will believe that I can beat him here," the reigning U.S. Open champion said on court.
"It will be tough but I'm ready for this. I dreamed of this since I started to play tennis, to play in a final here. It's not time to be afraid, I will go for it."
