The selection was announced from the stage constructed on the steps of the Philadelphia Museum of Art.
Barnett gives the Eagles a strong edge rusher. He had 32 sacks in three seasons.
"I just love football, I love everything the game brings. I love the contact, I love playing with 10 other guys on defense, I love everything about it," said Barnett at an introductory news conference on Friday.
"But me being first round pick doesn't mean anything. I have to come into work and gain respect first," he continued.
Philadelphia upgraded its offense in free agency and entered the draft with obvious needs on defense. After releasing former Pro Bowl defensive end Connor Barwin, the Eagles added veteran Chris Long.
Barnett broke Hall of Famer and former Eagles star Reggie White's sack record at Tennessee.
VIDEO: Jeff Skversky interviews Derek Barnett on the red carpet
"I heard the fans are very passionate, and I know I'm going to an organization with a lot of great players. I can't wait, I'm ready to get to work," Barnett said in a news conference after his selection on Thursday night. "Everyone's telling me to enjoy this moment, but I love football and I'm ready to get back to what I love to do.
"He stands for what we want to be and I think everyone in the city will see what kind of person he is, what kind of player he is," said Executive Vice President of Football Operations Howie Roseman. "Unbelievably high character, unbelievable worker, and tremendously talented and productive."
Reaction on the Ben Franklin Parkway was mixed.
"Exciting. Very exciting, though I will say I was hoping for a wide receiver, but a lot of them had already gone earlier," said Lesley Lewis.
"Hopefully he pans out to get a lot of sacks, because I really wanted a cornerback right there," said Lamar Reddick.
"Not a fan. Not a fan, I wanted a cornerback. Horrible pick. I wanted a cornerback bad, man," said C.J. Stiles.
DE Derek Barnett - Tennessee— Jeff Skversky 6abc (@JeffSkversky) April 28, 2017
-13 sacks last season - ONLY 5 players in country had more
-broke Reggie whites sack record at Tennessee pic.twitter.com/x9Z5kpGxBR
Send a breaking news alert to Action News
Report a correction or typo
Learn more about the 6abc family of apps