Dyson was drafted by the Royals in the 50th round with the 1,475th pick of the 2006 MLB Draft. He made his MLB debut on September 7, 2010.
Born and raised in McComb, Mississippi, Dyson attended McComb High School, where he starred in baseball and football as a running back. At McComb, Dyson earned All-Division honors but was passed over by most scouts due to his slight stature. Dyson later attended Southwest Mississippi Community College. At Southwest, Dyson tied the single-season record with seven triples and set a record with 47 runs.   
Early professional career
Dyson was drafted by the Royals in the 50th round, 1,475th overall, of the 2006 amateur draft.  He signed with the team for $5,000.  Dyson began his professional career that year, playing for the AZL Royals and hitting .273 with no home runs and 19 stolen bases in 51 games. He played in 10 games in 2007, all for the Burlington Bees, hitting .270.
He spent 2008 with the Wilmington Blue Rocks, hitting .260 with 39 stolen bases in 93 games. He split the 2009 season between the Bees (17 games) and Northwest Arkansas Naturals (63 games), hitting a combined .276 with 46 stolen bases. He began 2010 in the minor leagues, splitting the season between the AZL Royals, Blue Rocks, Naturals and Omaha Royals. He hit .299 with 24 stolen bases in 71 games.
Major league career
Dyson was first called up to the major leagues in September 2010, joining the Royals and getting some playing time in center field. He played in 18 games and hit .211 with nine stolen bases in 57 at-bats. He made the team out of spring training in 2011, and took on the role of a pinch running specialist. He is regarded as one of the faster outfielders in the game. 
With Melky Cabrera having a breakout season in center field, Dyson spent the majority of the season in Triple-A. When in the Major Leagues, he served as a late-inning pinch runner for Billy Butler and Brayan Pena. Dyson hit .205 in 44 at-bats, stealing 11 bases.  In the minors, he hit .279 with 38 stolen bases in 83 minor league games that year.
The Royals originally had Lorenzo Cain as their starting center fielder, however Dyson gained significant playing time as a result of injuries to Cain.
In 102 games, Dyson finished the 2012 season with 76 hits in 292 at-bats leading to a .260 batting average. He also had nine RBI, eight doubles, five triples, 30 walks, 52 runs scored and 30 stolen bases, further highlighting his speed and baserunning talent. He spent 15 games with the minor league Omaha Storm Chasers that year as well, hitting .333 with seven stolen bases.
In 2013, Dyson set a career best with 34 steals and had a slash line of .258/.326/.366. He furthered his role as a valuable player off the bench for late inning baserunning.
In spring training in 2014, Dyson tied for the major league lead in stolen bases with 10, while not being caught once.  He finished the regular season tied for third in the American League with 36 steals. He was often used as a late inning pinch runner and defensive substitute, taking over in center field while Lorenzo Cain would shift to right field taking the place of Norichika Aoki. He played in a career high 120 games and had a career high batting average (.269) and RBI total (24).
On January 28, 2015, the Kansas City Royals and Dyson avoided arbitration by agreeing to a one-year contract for $1,225,000. Dyson, who is expected to be the Royals' fourth outfielder, can also make $25,000 for reaching 350 plate appearances and $50,000 if he is chosen for the All-Star Game. 
In 2015, Dyson played an important role in the Royals win of the 2015 World Series against the New York Mets. The Royals were up 3 games to 1 in the fifth game of the World Series. In the 12th Inning, the Royals and Mets were tied at two runs each. After a single to right field, Dyson, known for his speed, pinch ran for Salvador Perez. Dyson proceeded to steal 2nd base. When Alex Gordon grounded out to first, Dyson got to third base. Then, Christian Colón singled to left allowing Dyson to reach home plate giving the Royals their first lead of the game. The Royals would finish the inning with a total of five runs, winning the game 7-2 and becoming the 2015 World Series Champions. 
Dyson has three older brothers and a younger sister, and was raised by Cecilia, his mother. The family lived in public housing until he was eight years old.  In January 2016, the city of McComb, Mississippi announced it was renaming one of its streets Dyson Drive to honor him.