Wawrinka came from a set down to defeat Federer 4-6 7-6 (7-5) 6-2 to claim his maiden ATP 1000 victory on the clay surface.
It was Wawrinka's first title since claiming Australian Open glory in January this year and Federer pleased for his fellow countryman.
"I'm very happy for Stan," he said. "It's a huge win for him after winning his first grand slam this year, to win his first Masters 1000.
"To take the opportunities when they're there, that's key in a tennis player's career.
"It was a great pleasure to share this moment with Stan. It was a tennis celebration on a beautiful court.
"I played with a lot of intensity during the past month. I'm happy that I can relax."
Federer now travels to Madrid and Rome for two more ATP 1000 events before the French Open next month, and the Swiss sees himself and Wawrinka as among the favourites for the title, along with Novak Djokovic and Rafael Nadal.
"I think we're right there," he said.
"We've put ourselves in (winning) positions time and time again.
"This was one of those weeks we were able to capitalise on it. Stan did the same at the Australian Open. I did it in Dubai. It's definitely a good start to the season for all four of us."