Jenkins grew up in Canada, where he excelled at baseball, basketball, and hockey, competing in Canada's highest amateur hockey league. Upon graduation from high school in the early 1960s, he signed with the Philadelphia Phillies. Originally a relief pitcher, he was converted into a starting pitcher shortly after being acquired by the Chicago Cubs in 1966. The following year he was one of the aces of the Cubs' staff, accomplishing the first in a string of six years with 20 or more wins per season.

From 1974 to 1981 Jenkins pitched for the Texas Rangers and the Boston Red Sox, compiling a record of 115 wins and 93 losses. In 1982 he returned to the Cubs, where he pitched for two more years before retiring.

A consistent pitcher with remarkable control, Jenkins is the only pitcher with more than 3,000 strikeouts to have fewer than 1,000 walks. Jenkins was one of the leading pitchers of his era, which included such stars as Bob Gibson (Gibson, Bob) and Tom Seaver. He finished his career with a record of 284 wins and 226 losses and with an ERA of 3.34. His 3,192 strikeouts place him 10th among the all-time leaders. He was elected to the Baseball Hall of Fame in 1991, the first Canadian to be so honoured.