Medvedev's fifth title of a stellar season and 20th overall leaves him as one of the top contenders for Roland Garros which begins on May 28.
The 27-year-old, who was out of the top 10 in February, is set to climb to number two in the world and will take the second seeding behind Carlos Alcaraz in Paris, with Novak Djokovic dropping down to number three.
Medvedev drew first blood in the first Rome final since 2004 not to feature 22-times Grand Slam champions Rafa Nadal or Djokovic, breaking in the 12th game where he met a feeble drop shot from Rune with a powerful drive to wrap up the first set.
Rune, at 20 the youngest finalist at the Foro Italico since Spaniard Nadal 17 years ago, broke to love in the first game of the second set and pounced again for a 4-3 lead after Medvedev hit back to level the scores.
But the aggressive world number seven appeared to run out of steam late in a physically demanding spell to hand the advantage back to Medvedev, who produced a tight hold thanks to two huge serves before closing out the victory in style.
"I always want to believe in myself and I always try to do my best as I want to win the biggest tournaments in the world," Medvedev, who had not won a match in Rome before this year's tournament, said.
"At the same time, honestly I didn't believe much I can win a Masters 1000 on clay in my career because usually I hated it and I didn't feel good on it, nothing was working.
"Before this tournament already in Madrid and Monte Carlo I was not feeling too bad. I didn't have any big tantrums and was like 'OK, let's continue' and here I felt amazing in practice.
"But then you need to play the toughest opponents in the world and try to make it. I'm really happy that I managed to do it and prove to myself and everybody that I'm capable."
