The third seed and six-times champion was at his imperious best on Centre Court against the 26th-seeded Russian, picking him off at will to set up a last-four showdown with defending champion Novak Djokovic.
"I thought I played great out there today," Federer said in a courtside interview after a 14th successive win over Youzhny.
"My game maybe suits up well against his.
"He was down in all the sets rather quickly. I am extremely happy to be back in the semi-finals here at Wimbledon."
Federer and Youzhny were watched from the Royal Box by the Duke and Duchess of Cambridge and former Wimbledon champions Andre Agassi and Steffi Graf.
"I think it's inspiring when royalty and other legends of the game come to watch," Federer said. "It's great for tennis."
Federer, knocked out in the quarter-finals at the All England Club the last two years, roared into a 4-1 lead and after a short rain delay wrapped up the first set in 28 minutes.
The Swiss maestro broke in the first game of the second set with the aid of a lucky net-cord and, showing no sign of the back injury which hampered him in his quarter-final win over Xavier Malisse, he sauntered into a 2-0 lead.
With the sun making a rare appearance at the tournament, Federer broke Youzhny again at the start of the third set.
The Russian let out a huge roar of frustration when he failed to take advantage of a break-point but he made far too many unforced errors to get back into the match.
Federer wasted three match points on Youzhny's serve but he quickly earned himself two more and took the first with a deft angled volley to wrap up victory in an one hour 32 minutes.