They agreed on a five-year, fully guaranteed contract worth $22,190,498, a league source told ESPN NFL Insider Adam Schefter.
The contract includes a signing bonus of $14,518,544, and Fisher will get $10 million of that paid within five days, the source said.
His base salary will be $405,000 in 2013; $495,000 with a training camp roster bonus of $918,659 in 2014; $585,000 with a roster bonus of $1,837,318 in 2015; and $675,000 with a roster bonus of $2,755,977 in 2016. The fifth-year option belongs to the Chiefs under the terms of the collective bargaining agreement.
Fisher's contract is on par with the two previous No. 1 picks that have been signed since the NFL instituted a new rookie wage scale with the most recent CBA.
"I'm happy to be here and happy to get to work," said Fisher, who arrived at training camp in time to pass a conditioning test and participate in the first full-squad workout.
"I just wanted to get the deal done," he said.
Fisher was diligent in attending the Chiefs' entire offseason program, even though he hadn't signed a contract. But he was absent from three days of rookie practice in St. Joseph, Mo., before joining the rest of the team in camp for Friday's public workout.
Chiefs coach Andy Reid said he wasn't concerned that Fisher wouldn't get to camp, but still expressed a sense of relief to have the big offensive tackle in the fold.
"I think it worked out well for Fish, and at the same time, it's good for our organization," Reid said. "Heck, he's a good football player, and we wanted him in here. We didn't want him to miss any reps, and he was able to do that.
"Until the fish is in the boat, you don't count it caught, right? That's how it works."
Fisher was only the third offensive tackle picked No. 1, joining Orlando Pace (1997) and Jake Long (2008), since the 1970 merger of the NFL and AFL. The 6-foot-7, 306-pound Fisher also became the first Mid-American Conference player selected at the top of the draft.
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."
While he may not be as polished as Joeckel, who went second overall to Jacksonville, Fisher is considered to be more athletic and the Chiefs believe he has a greater upside.
"When you're the No. 1 pick, you're signing for more than one year, and you want both sides to be happy and content," said Smith, who was the No. 1 overall pick of San Francisco in 2005.
"It's also important to get in here," Smith said. "When you're the No. 1 pick, you're probably not going to be sitting for long, you know? In Eric's case, he's not at all."
Most project him as a future left tackle, but Fisher will start off on the right side because the Chiefs opted to give veteran Branden Albert the franchise tag.
Albert will play this season under a one-year deal worth about $9.3 million, but his future beyond that is uncertain. The Chiefs have expressed interest in signing the durable left tackle to a long-term deal, but the two sides have been unable to close a wide gap in negotiations.
That means that Fisher could eventually replace Albert in protecting Smith's blind side in a revamped offense under Reid.
"I just try to play football. I know how to play football and do what I've done the last four years, because that's what has gotten me here," Fisher said during offseason workouts.
"I'm just trying to play offensive line," he said. "I really love everything that comes with it. It's a different territory in there. It's a very similar system to what I ran in college."
Information from The Associated Press was used in this report.