Clady suffered a Lisfranc joint tear to his left foot late in the Broncos' 41-23 Week 2 victory over the New York Giants and will undergo surgery, the team announced.
The Broncos spent much of Tuesday working Clady through several medical exams.
Justice will receive the veteran minimum plus another $350,000 in incentives, a league source told ESPN. He was a second-round pick of the Philadelphia Eagles in 2006. He started 12 games for the Indianapolis Colts last season.
Clady, a three-time Pro Bowl selection, signed a $57.5 million deal just before training camp, with about $33 million of the contract guaranteed. He had started 82 consecutive regular-season games since being drafted by Denver in the first round in 2008.
"Stepping up into a role like this, it's not going to be hard for me to adjust,'' said Clark, who received a two-year contract extension on Monday. "It's not about filling a guy's shoes for me. It's about me creating my legacy, just helping the team the best way I can and doing my job.''
Broncos offensive line coach Dave Magazu said he's confident Clark can fill in with Clady out.
"You're not going to replace him, but Chris Clark did a great job all spring and in the preseason, so he's had plenty of work," Magazu said, according to the team's website. "It's not like he's going in unprepared or not knowing what's going on. So everybody should feel comfortable [and] go with the mentality next guy up and let's go to work."
The Broncos scored 60 touchdowns and averaged 6.0 yards per play with Clady on the field the past two seasons, according to ESPN Stats & Information. On the 33 snaps he wasn't on the field, Denver averaged 3.0 yards per play and didn't score a touchdown.
This isn't the first time the Broncos have had to reshuffle the offensive line in front of quarterback Peyton Manning. Earlier this summer, the team lost center Dan Koppen for the year to an ACL injury. The offense hasn't missed a beat with Manny Ramirez snapping the ball to Manning, averaging 45 points a game.
"You want your quarterback to feel comfortable when he's back there, knowing that the person that's responsible for that is going to make the right calls and the right adjustments when the time comes,'' said Ramirez, who also signed a two-year extension last week. "I think I've filled that role so far and I'm just going to continue to improve it.''
ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.