Otis was initially drafted by the Boston Red Sox in 1965 as a shortstop. However, he put in some time in the outfield, third base, and first base while playing in the minors. In November 1966, the Mets drafted him and jumped him all the way to Class AAA for 1967. He saw some time with the Mets late in the 1967 season, but spent 1968 in AAA again before making the major league roster for 1969.When the Braves asked for Otis when trying to trade Joe Torre, the Mets refused and Torre wound up going to the St. Louis Cardinals instead.

However, Otis immediately clashed with Mets manager Gil Hodges, who tried to make him a third baseman. After four games, Otis was sent back to the minors for a month. At the end of the season, Royals general manager Cedric Tallis sent third base prospect Joe Foy to the Mets, in exchange for the young Otis.

Foy was bogged down by drug problems and was out of baseball by 1971. Meanwhile, the Royals immediately moved Otis to center field, and he became the starter for most of the 1970s.

He made the American League all-star team each of his first four years with the team and won three Gold Gloves. His speed worked well with the Royals' team philosophy of speed and defense. On September 7, 1971, he became the first player since 1927 to steal five bases in one game. He led the American League with 52 stolen bases that year. Otis scored the final run ever at Kansas City's Municipal Stadium in the 5th inning on October 4, 1972.

Otis was very much a player of his time, utilizing his speed on both offense and defense. He was one of the top players of that time, combining power, speed, on-base percentage and defense. He hit as many as 26 homers in a season, knocked in 90 runs or more three times, twice led the AL in doubles and once in stolen bases with 52, compiling a career total of 341 steals, with just 93 caught stealing marked against him. Otis was known as a clutch performer, and consistently produced for the Royals as the team became a perennial contender.

He was a crowd favorite, as Royals fans yelled "AO" as the slim center fielder came to bat. He was the team's first star, but gradually yielded that role to George Brett by the mid-1970s.

Otis was also a decent person off the field. On September 18, 1977, Otis helped eight youths who were stranded after a Royals game had been rained out when flooding had prevented the boys' parents picking them up. "If it was my kids," Otis said, "I would have wanted someone to do something for them, too."

Otis played on national TV many times, and has his greatest week in the glare of the spotlight. He hit .478 with 3 home runs and 7 runs batted in the 1980 World Series and set a record for putouts in a game by an outfielder in Game 3, a contest in which he also homered.

But his offense started to decline, in part due to a hand injury. By the late 1970s and early 1980s, his fielding skills had diminished, and he lost his center field job to Willie Wilson near the end of his long run with the Royals. In 1983, he left the team before the season ended when told he was not in the Royals' future plans.

He spent most of 1984 in the National League with the Pittsburgh Pirates at the close of his career. It was a quiet end to a successful career. In a 17-season career, Otis posted a .277 batting average, with 193 home runs and 1,007 RBI in 1,998 games while stealing 341 bases.

He worked for the Padres and Rockies as a hitting instructor, and has retired to Las Vegas. Otis still attends Royals reunions, and dons a uniform to play in alumni games.

In the early 1990s Otis admitted that he had used a corked bat during part of his Major League career.