The Pro Bowl safety has been staying away from the team after the sides couldn't agree on a long-term contract extension last month. Berry was slapped with the franchise tag, but hasn't signed the tag, so he's not currently under contract and therefore can't be fined for missing camp.
Berry's absence will end before the preseason.
NFL Media Insider Ian Rapoport first reported Friday that Berry will report to the Chiefs' facility early next week to sign his tender, per a source with knowledge of the situation.
Coach Andy Reid told NBC Sports Radio on Friday morning he has no concerns about Berry coming in out of shape and expects the safety to start the season on the field.
"Eric's one of our good players and he's in the business side of it right now," Reid said. "This is all part of the profession, so I get it. But I also know when he comes in he's going to be in great shape, he'll be able to get himself back before the first game and be ready to go because that's the way he trains in the offseason and the kind of shape he keeps himself in."
With the deadline for tagged players to receive a new contract passed (July 15), Berry can't get a long-term deal until after the Chiefs' season ends. He'll play 2016 on the $10.806 million tag.
Berry proved his worth last season, recovering from cancer to win the Comeback Player of the Year award. A defense that is still dealing with injuries in its front seven will welcome the rangy safety back with open arms.