The 6-foot 7-inch, 306-pound Fisher became the first offensive tackle to go number one since Jake Long was chosen by the Miami Dolphins in 2008 and only the fourth tackle ever taken first.
Fisher added his name to a select list that also included Orlando Pace (1999 St. Louis) and Ron Yary (1968 Minnesota), the only other offensive tackles named as the top overall picks.
"This is so surreal. This is a dream come true," Fisher said from the Radio City Music Hall stage after being congratulated by NFL commissioner Roger Goodell.
The lack of interest in offensive playmakers also strained the usual sensibilities as the first skills player, wide receiver Tavon Austin, was not taken until the eighth pick by St. Louis and he was alone in that distinction for another eight until quarterback E.J. Manuel was taken by Buffalo at No. 16.
Noted for his athleticism, Fisher played quarterback and linebacker in his first two seasons of high school football in Michigan before moving to the offensive line, whose practitioners dominated the top of the draft.
Picking second in the worst-to-first order of selection, the Jacksonville Jaguars made it back-to-back tackles at the top by taking Luke Joeckel of Texas A&M.
Joeckel, winner of the Outland Trophy awarded to the best college football interior lineman by the Football Writers Association of America, was followed two picks later by tackle Lane Johnson of Oklahoma, taken by the Philadelphia Eagles.
"Three tackles in four picks. That's a lot of love for the big boys up front, which we usually don't get," said Fisher, who rocketed up the draft charts with his late season performances and eye-catching workouts.
The Chiefs had the first pick of the draft, the primary way NFL teams build their rosters, by posting the league's worst record last season, going 2-14.
When tackles were not tabbed, teams looked to pass rushers at the start of the draft.
Miami traded their first-round pick (No. 12) and second-round pick to Oakland for the third choice, which they used to snare defensive end Dion Jordan of Oregon.
The fifth and sixth picks were also on the defensive side with Detroit taking defensive end Ezekiel Ansah of Brigham Young, a native of Accra, Ghana, followed by Cleveland's selection of defensive end/linebacker Barkevious Mingo of LSU.
Austin finally dented the draft board for the offensive skills players when St. Louis traded for Buffalo's number eight slot and used it to grab the wide receiver from West Virginia.
The first quarterback taken was something of a surprise as Florida State signal caller E.J. Manuel jumped over other higher-profile passers when Buffalo nabbed him at 16th.
Manuel and Austin were the only offensive skill players taken through the top 20 picks, which saw eight offensive linemen selected.
Rounds two and three will be held on Friday, with the last four rounds on Saturday.
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