Financial terms of the deal weren't disclosed. The Eagles released wide receiver Blue Cooper to make roster room for Graham, who was the team's last remaining unsigned draft pick.
"It feels good because I really wanted to get to training camp, and coach (Andy) Reid really wanted me to get to camp, and now it's time to show them why they picked me," Graham said in a statement released by the Eagles. "I have a lot of work to do, but I'm ready to go."
The Eagles hold their first training-camp practice Friday afternoon, and Graham could attend.
The Eagles traded up 11 spots in the April draft to grab Graham, a 6-foot-2, 268-pound lineman for Michigan. He had 64 tackles -- 26 for a loss -- and 10.5 sacks during his senior season with the Wolverines.
"I'm really glad that we were able to work well with Joel Segal (Graham's agent) on getting this deal done," Eagles president Joe Banner said in the statement. "We're really excited to get Brandon on the field tomorrow in time for the start of the first full-team practice."
The Associated Press contributed to this report.