Albert would have become a free agent this offseason had he not received the franchise designation from the Chiefs. He signed the contract worth $9.82 million late last month.
The Chiefs mainly spent their first day of workouts in meetings, where coach Andy Reid laid out the groundwork for the offseason program and the coaching staff handed out playbooks, though several players said they already feel a more positive vibe at Arrowhead Stadium.
Kansas City struggled to a 2-14 finish last season.
The Chiefs also announced they've re-signed reserve linebacker Edgar Jones and released linebacker Andy Studebaker, who contributed mostly on special teams.