The deal is expected to be in the $22 million range, which would put it on par with the two previous No. 1 picks to have been signed since the NFL instituted a new rookie wage scale with the most recent collective-bargaining agreement.
Fisher was expected to report to training camp Friday in St. Joseph, in time for the team's first full-squad workout later in the day. He attended the Chiefs' entire offseason program, but missed three days of practice earlier this week involving his fellow rookies.
Fisher and another tackle, Texas A&M's Luke Joeckel, were widely considered the top offensive linemen available in this year's draft. The Chiefs opted to nab Fisher with the first No. 1 pick in franchise history, securing a bookend tackle for new quarterback Alex Smith.
"Watching three tackles come off in the first four picks, I think people knew they would go high, but nobody was expecting that," Chiefs chairman Clark Hunt said after the draft. "It shows that a lot of teams know that you have to win in the trenches, and we certainly feel that way."