Eckersley grew up in the San Francisco Bay area, rooting for both the San Francisco Giants and the Oakland Athletics. He was a quarterback at Washington High School in Fremont until his senior year, when he gave up football to protect his throwing arm from injury. He won 29 games as a pitcher at Washington, throwing a 90 mph fastball and a screwball.
Eckersley was drafted out of high school by the Cleveland Indians in the third round of the 1972 amateur draft and was disappointed that he was not drafted by the Giants. He made his MLB debut on April 12, 1975. He was the American League Rookie Pitcher of the Year in 1975, compiling a 13–7 record and 2.60 ERA. His unstyled, long hair, moustache, and live fastball made him an instant and identifiable fan favorite. Eckersley pitched reliably over three seasons with the Indians.
He threw a no-hitter on May 30, 1977 against the California Angels. Two batters reached base in the game, one on a walk in the first inning and the other on a third strike that was a wild pitch. He earned his first All-Star Game selection that year and finished the season with a 14-13 win-loss record.
Eckersley was traded with Fred Kendall on March 30, 1978 to the Boston Red Sox for Rick Wise, Mike Paxton, Bo Díaz, and Ted Cox. Over the next two seasons, Eckersley won a career-high 20 games in 1978 and 17 games in 1979, with a 2.99 ERA in each year. However, during the remainder of his tenure with Boston, from 1980 to 1984, Eckersley pitched poorly. His fastball had lost some steam, as demonstrated by his 43–48 record with Boston. He later developed a great slider.
Eckersley was traded on May 25, 1984 with Mike Brumley to the Chicago Cubs for Bill Buckner, one of several mid-season deals that helped the Cubs to their first postseason appearance since 1945. Eckersley performed poorly in his sole start for the Cubs in their NL Championship Series with the San Diego Padres.
Eckersley remained with the Cubs in 1985, when he posted an 11–7 record with two shutouts (the last two of his career). Eckersley's performance deteriorated in 1986, when he posted a 6–11 record with a 4.57 ERA. After the season, he checked himself into a rehabilitation clinic to treat alcoholism. Eckersley noted in Pluto's book that he realized the problem he had after family members videotaped him while drunk and played the tape back for him the next day.
Eckersley was traded again on April 3, 1987 to the Oakland Athletics, where manager Tony La Russa intended to use him as a set-up pitcher or long reliever. Indeed, Eckersley started two games with the A's before an injury to then-closer Jay Howell opened the door for Eckersley to move into the closer's role. He saved 16 games in 1987 and then established himself as a dominant closer in 1988 by recording a league-leading 45 saves. He recorded saves in all four games as the A's swept the Red Sox in the 1988 ALCS (which was matched by Greg Holland in the 2014 ALCS), but he found himself on the wrong end of Kirk Gibson's 1988 World Series home run as the A's lost to the Dodgers in 5 games. In the 1989 World Series he secured the victory in Game Two, and then earned the save in the final game of the Series, as the A's swept the San Francisco Giants in four games.
Eckersley was the most dominant closer in the game from 1988 to 1992, finishing first in the A.L. in saves twice, second two other times, and third once. He saved 220 games during the five years and never posted an ERA higher than 2.96. He gave up five earned runs in the entire 1990 season, resulting in a microscopic 0.61 ERA. Eckersley's control, which had always been above average even when he was not otherwise pitching well, became his trademark; he walked only three batters in 57.2 innings in 1989, four batters in 73.1 innings in 1990, and nine batters in 76 innings in 1991. In his 1990 season, Eckersley became the first relief pitcher in baseball history to have more saves than baserunners allowed (48 SV, 41 H, 4 BB, 0 HBP). In a statistical anomaly, he had exactly the same WHIP and ERA: both were 0.613636364.
After the 1994 season, the Athletics elected not to exercise a $4,000,000 option on Eckersley, making him a free agent. The team indicated that it would be interested in signing him at a lower salary. Oakland signed him to a one-year contract in early April 1995. His contract was the first MLB deal after a three-month signing ban resulting from a labor dispute between owners and the players union.
When Tony La Russa left the A's after the 1995 season, he became the St. Louis Cardinals' new manager and arranged to bring Eckersley along with him. Eckersley continued in his role as closer and remained one of the league's best, but following the 1997 season, he signed on with the Red Sox for one final season.
Eckersley announced his retirement in December 1998. He commented on his career, saying, "I had a good run. I had some magic that was with me for a long time, so I know that I was real lucky to not have my arm fall off for one thing, and to make it this long physically is tough enough. But to me it's like you're being rescued too when your career's over. It's like, 'Whew, the pressure's off."
He retired with a career 197-171 win-loss record, a 3.50 ERA and 390 saves. Eckersley's career saves total ranks sixth on the all-time list as of early 2014. Eckersley had appeared in more games (1,071) than any pitcher in MLB history, though he ranks fifth all-time as of early 2014.
Eckersley works as a studio analyst for the Boston Red Sox on NESN, where he primarily provides post-game coverage, analyzing the strengths and weaknesses of the team's play. He also has a multi-year deal with TBS to serve as an analyst for their post-season coverage. In the spring of 2009, regular NESN commentator Jerry Remy took time off for health reasons. Eckersley filled in for Remy, providing color commentary alongside Don Orsillo. Since then, Eckersley has been the primary substitute for Remy when he is unavailable, most recently filling in for the remainder of the 2013 season when in early August, Remy's son, Jared, was indicted on murder charges, after which, Jerry chose to take off the rest of the year.
Eckersley was married to his first wife Denice until she left him for Rick Manning, his then-Cleveland Indians teammate, in 1978; the affair precipitated Eckersley's trade to the Red Sox that year. Two years later, Eckersley married model Nancy O'Neil. They divorced shortly after his retirement from baseball. His third wife, Jennifer, is a former lobbyist and manages Eckersley's business and charitable affairs.
Eckersley's brother, Wally "Glenn" Eckersley, was sentenced to 40 years in prison in 1989 following a conviction for attempted murder and kidnapping. Dennis Eckersley testified at his brother's trial to show that alcoholism ran in his family.