Justice's deal is worth $18.15 million, including a $6 million signing bonus, a league source told ESPN's Adam Schefter.
The team announced the deal on Tuesday. Justice could have become an unrestricted free agent after this season.
A second-round pick in 2006, Justice has started every game this season after starting only one in his first three years in the NFL. He replaced Shawn Andrews, who didn't take a snap and was placed on injured reserve with a season-ending back injury.
Jon Runyan had started every game at right tackle for the Eagles since 2000, but he wasn't re-signed after last season and remains a free agent.
Information from The Associated Press was used in this report.