Medvedev, the world number five, won 6-2, 6-3 against his 73rd-ranked opponent.
The Russian joins Alexander Zverev, who will become world number one in the next ATP rankings on Monday, Alcaraz, and Ben Shelton in the season-closer, which will run November 15-22 in Turin.
Medvedev has only missed the cut for the ATP Finals once since 2019.
On Friday, he closed out on his second match point on the Frenchman's serve.
Since his elimination in the round of 16 at the US Open in early September by Frances Tiafoe, Medvedev has won tournaments in Hangzhou and Almaty, and reached the semi-finals of the Shanghai Masters 1000 and the Beijing ATP 500.
Standing between him and the final in the Austrian capital is seven-time Grand Slam champion Alcaraz.
The 23-year-old Spaniard beat American Tommy Paul 6-4, 7-6(2) in the quarter-finals.
"I think I played great tennis," Alcaraz said after extending his record to 14-0 in 500-level tournaments this season.
"I would say, overall, just happy for the battle and happy I found my way to get the win in straight sets."
Later on, new world number one Zverev joined Alcaraz and Medvedev in the final four with a dominant 6-0, 6-2 win overArthur Fery.
Fery, who received treatment from the physio in the closing stages of his second-round win against Lorenzo Musetti on Thursday, appeared to be physically hindered from the first game against Zverev.
The German will next face Australian fifth seed Alex De Minaur, who beat Matteo Berrettini in straight sets.
De Minaur beat Zverev at the Laver Cup, and with him still standing a chance of making the ATP Finals, he has plenty to play for.
