Johnson's deal runs through 2021. Sources told ESPN NFL Insider Adam Caplan that it's worth $63 million, with $35.5 million guaranteed.
"I want to be here the rest of my career," Johnson said. "A lot of the guys in the locker room are like my brothers. It's where I want to be."
The Eagles took Johnson with the No. 4 pick in the 2013 NFL draft. He has started 45 games, including a playoff game, in his three seasons with the Eagles. Johnson was suspended for four games at the beginning of the 2014 season for violating the NFL policy on performance-enhancing drugs.
Johnson, 25, started 43 games at right tackle. He started two games at left tackle in 2015 because of injuries to Jason Peters. The Eagles' plan all along has been to move Johnson to left tackle when Peters, who turned 34 last week, is gone.
"I think that's what they drafted me for," Johnson said. "Jason Peters is probably the best tackle of all time -- one of them. He's taught me so much. I'm just going to continue to do that until that time comes."
Johnson has said he is comfortable at either tackle position. Left tackles are typically paid more than right tackles. That is reflected in Johnson's new deal, which includes more guaranteed money than all but three offensive tackles in the league.
"It's definitely a fair deal," Johnson said. "I'll be the highest-paid right tackle. If it comes to left, I think it's a fair deal. Wherever I'm playing, I'm going to give 110 percent and give them their money's worth."
Johnson, 25, played quarterback at Kilgore (Texas) College before transferring to Oklahoma. He switched to tight end and, briefly, defensive end at Oklahoma, then moved to right tackle as a junior. He played left tackle during his senior season.