Croatia awaits Russia in Sunday's final on the indoor hard court at the Madrid Arena after eliminating Novak Djokovic's Serbia on Friday. Both Russia and Croatia will be aiming for a third Davis Cup title.
With four players ranked in the top 30, Russia was favored against a German team playing without star Alexander Zverev.
Medvedev enters the final, where he should be slated to face Croatia's No. 1 Marin Cilic, after not dropping a single set at the tournament.
The reigning U.S. Open champion had little trouble commanding his serve against Struff, and it seemed only a matter of when he could pounce on a mistake by the German.
Struff hung tight with Medvedev until he dug himself into a 0-40 hole at 4-4 in the first set. He saved two break points before sending an approach shot into the net to fall behind. Medvedev then held his serve easily to take a one-set lead.
Medvedev pressed home his advantage after going up a break at 3-2 in the second set.
He needed just 50 minutes to see off Koepfer.
Rublev smashed in six aces to ease to a set advantage. Koepfer then faded fast, ceding breaks in his three service games of the second set as Rublev cruised to victory.
The Russian team is officially being called RTF (Russian Tennis Federation) in the competition amid its ongoing doping suspension in international sport.