Luis Tiant was the only child of Luis Tiant, Sr. and Isabel Vega. From 1926 through 1948, the senior Tiant was a great left-handed pitcher for the New York Cubans team, and his heroics were followed by hundreds of thousands of Cubans. Luis Jr. followed his father's footsteps at an early age, joining both the local Little and Juvenile baseball leagues until he starred for the Havana team and was picked up for the Cuban Juvenile League All-Star team in 1957. His talent was recognized by former Cleveland Indians star, Beto Avila, who was scouting for talent in Cuba. Avila recommended him to the Mexico City Tigers of the Mexican League. Tiant was signed for $150 a month, and for the next three years he divided his time with the Tigers and for the Havana Sugar Kings in the International League. At the end of the summer of 1961, and under Avila recomendations, Cleveland purchased Tiant's contract for $35,000. But with the rise of Fidel Castro's regime in his native Cuba, it was impossible for Tiant to return home. He would not see his parents for 14 years.

Tiant progressed through the Indians farm system and got the call to the big club after a 15-1 record at Triple-A Portland. On, July 19, 1964, Tiant debuted with a four-single, 11 strikeouts, 3–0 shutout victory against the defending AL Champion New York Yankees at Yankee Stadium. The losing pitcher was future Hall of Famer Whitey Ford. Tiant finished his rookie season with a 10-4 record, 105 strikeouts, and a 2.83 ERA in 19 games.

In 1966 Tiant pitched four straight shutouts on his way to 12 wins and a 2.79 ERA. But Tiant really broke through in 1968, after he altered his delivery so that he turned away from the home plate during his motion, in effect creating a hesitation pitch. Twisting and turning his body into unthinkable positions, Tiant would spend more time looking at second base than he did the plate as he prepared to throw. In that season, he led the league in ERA (1.60), shutouts (9), hits per nine innings (5.3), strikeouts per nine innings (9.22, more than a batter an inning), while finished with a 21-9 mark. Beside this, opposing hitters batted just .168 off Tiant, a major league record, and on July 3 he struck out 19 Minnesota Twins in a ten-inning game, setting an American League record for games of that length. His 1.60 ERA was the lowest in the American League since Walter Johnson's 1.49 mark during the deadball era in 1919.

After an injury-plagued season in 1969, Tiant was traded to the Twins in a multi-player deal that brought Graig Nettles to the Indians. With Minnesota, Tiant began 1970 with six wins, but then he fractured his right scapula and virtually ended the season. He showed little promise in the 1971 spring training, but was released. The Braves signed him to a minor league contract to play with their Triple-A Richmond, but he gave up after a few weeks. Tiant eventually landed in Boston, and despite struggling with a 1-7 record, 4.88 ERA, he would soon become one of the greatest and most beloved pitchers in Red Sox history and a great idol in Boston.

Starting to be known as "El Tiante" at Fenway Park, in 1972 Tiant regained his old form with a 15-6 record and led the league with a 1.91 ERA. He would win 20 games in 1973 and 22 in 1974. Though hampered by back problems in 1975, he won 18 games for the American League Champion Red Sox and then excelled for Boston in the postseason. In the playoffs he defeated the three time defending World Champion Oakland Athletics in a 7-1 three-hitter complete game, then opened the World Series against the Cincinnati Reds. His father and mother, having been allowed to visit from Cuba under a special visa, were in Fenway Park that game to watch his son defeat The Big Red Machine in a 6-0 five-hit shutout. Tiant won Game 4 as well (his second complete game in the series) and had a no-decision in Game 6, which has been called the greatest game ever played, after Carlton Fisk's dramatic game-winning walk-off home run in the 12th inning.

Tiant went 21-12 in 1976, 12-8 in 1977, and 13-8 in 1978. At the end of that season, he signed as a free agent with the Yankees. Tiant compiled a 21-17 record in New York over two seasons from 1979-80. He finished his career after two brief stints for the Pirates and Angels.

In his 19-season career, Tiant compiled a 229-172 record with 2416 strikeouts, a 3.30 ERA, 187 complete games, and 49 shutouts in 3486.1 innings. He was inducted to the Boston Red Sox Hall of Fame in 1997.

Tiant has fallen short the past few years on being selected to the Hall of Fame. Well known for his great pitching, charisma, and as an avid cigar smoker, he decided to launch his own line of cigars formulated and designed by him, being named after his nickname, El Tiante.

Luis Tiant currently resides in Boston.