Dalglish signed a provisional contract with Celtic in May 1967. Celtic manager Jock Stein sent Sean Fallon to see Dalglish and his parents at their home; on hearing that Fallon was at the door, Dalglish rushed upstairs to remove the Rangers posters from his bedroom walls. In his first season Dalglish was loaned out to Cumbernauld United, for whom he scored 37 goals. During this time he also worked as an apprentice joiner. By the following year Dalglish was a full professional and a regular member of the highly rated Celtic reserve team that became known as the Quality Street Gang, due to its having a large number of future Scottish internationals, including Danny McGrain, George Connelly, Lou Macari, and David Hay. Dalglish made his first-team competitive debut for Celtic as a substitute in the 1968 Scottish League Cup quarter-final tie against Hamilton Academical. Dalglish was in the stands when the Ibrox disaster occurred at an Old Firm match in January 1971, when 66 Rangers fans were killed. On 17 May 1971, he played for Celtic against Kilmarnock in a testimonial match for the Rugby Park club’s long serving midfielder, Frank Beattie. Dalglish scored six goals for Celtic in a 7–2 win.
By the 1971–72 season, Dalglish had become established in the Celtic first team. He scored his first goal for the club in a major competition, a penalty, in a 2–0 Scottish League Cup tie win over Rangers at Ibrox in August 1971, and that season went on to score 23 league and cup goals in 49 appearances. The following season Dalglish was Celtic’s leading scorer, with 39 goals in all competitions. He was made Celtic captain in the 1975–76 season, during which Celtic failed to win a trophy for the first time in 12 years, after Stein was badly injured in a car crash and missed most of the season. On 10 August 1977, after making 320 appearances and scoring 167 goals for Celtic, Dalglish was signed by Liverpool manager Bob Paisley for a British transfer fee record of £440,000. Dalglish’s departure was unpopular with the Celtic fans, and when he returned in August 1978 to play in Stein’s testimonial, he was booed by a large contingent of Celtic supporters.