Logan fills the void expected to be left by Dontari Poe, who is currently making visits to other teams. He is meeting with the Jaguars on Monday after visiting the Colts on Sunday. He is next scheduled to visit the Falcons.
The Chiefs decided against using the franchise tag on Poe despite having the option to do so after signing safety Eric Berry to a long-term contract.
"Eric Berry got a pretty substantial amount,'' Chiefs coach Andy Reid said at the NFL scouting combine in Indianapolis. "I'm not sure what's left in the purse."
The Chiefs would have had to offer Poe a one-year contract worth $13,387,000 if they had franchised him.
Logan, 27, is a strong, athletic defensive tackle who is above average against the run and has a knack for penetrating into the backfield to create havoc. Appearing in 13 games last season, Logan, who missed time with a groin injury, finished with five tackles for loss, 2.5 sacks, nine hurries and two forced fumbles.
Paired with Fletcher Cox, Logan formed a formidable duo at tackle since he was drafted in the third round out of LSU in 2013. While the Eagles had interest in keeping them together, it became difficult financially after the team gave a six-year, $102.6 million deal to Cox last June. Logan appeared in 59 out of a possible 64 games during his four years with the Eagles, posting 163 tackles (45 for loss) and 5.5 sacks.
Poe, who has been selected twice for the Pro Bowl, totaled 10.5 sacks in 2013 and 2014 and has 13 in his five-season NFL career.
He has been a workhorse for the Chiefs, missing only two games in his career because of injury. He also played a lot of snaps for a defensive lineman, but the Chiefs usually found him too valuable in both running and passing situations to provide him much relief.
Information from ESPN's Adam Teicher and Tim McManus contributed to this report.