Reilly joined Hibs in 1946, despite interest from their city rivals Hearts.[4] He quickly established himself in the Hibernian team, scoring his first goal against Queen of the South. He netted the first of 18 hat-tricks for Hibs in 1947, also against Queen of the South. He made his league debut as a 17-year-old in the 1946–47 season.[4] Reilly was a fringe player in the 1947–48 season as Hibs won the league championship, playing in insufficient games to earn a winners' medal.[4] It was reported that Reilly and Johnny Aitkenhead might be loaned to Edinburgh derby rivals Hearts, who were battling against relegation that season.[5]
Reilly became a first team regular during the following season, after Willie Ormond suffered a broken leg.[4] He earned his first selection for Scotland that season, playing and scoring in a 3–1 win against England at Wembley.[4] Later that year, the Famous Five were fielded together in a match for the first time.[4] The forward line were used regularly for the first time during the 1949–50 season.[4] The team earned 49 league points, more than in their championship-winning seasons, but lost out on the championship that season by a single point to Rangers.[4] That season also provided a major disappointment in Reilly's international career, as Scotland qualified for the 1950 FIFA World Cup, but the SFA refused to send the team to Brazil because they had failed to win the 1950 British Home Championship.[4]
By the early 1950s, Hibernian were the most feared force in Scottish football as they won back-to-back league championships in 1951 and 1952. Reilly was instrumental in both triumphs, finishing top scorer in the 1951–52 triumph. Hibs finished second to Rangers in 1953 and the club's fortunes started to go into decline, although Reilly continued to perform well.[4] He missed out on selection for the 1954 FIFA World Cup due to suffering from a bout of pleurisy.[4]
Reilly almost quit football after a row with Hibernian after manager Hugh Shaw refused him a testimonial match.[4] Reilly submitted a transfer request that was accepted by the board of directors,[4] but the matter was eventually resolved.[4] During the dispute, which lasted four months, Reilly took a job outwith football to support his family.[4] The SFA brokered a compromise that allowed Reilly to resume playing, while retaining his other income.[5]
Reilly continued to score goals frequently after he returned to the Hibs side, and he featured in the side that participated in the first season of the European Cup.[4] Injuries were beginning to make his appearances more intermittent, with a knee injury forcing his retirement from the game in 1958.[4] He made his final Scotland appearance against England in 1957, but failed to score at Wembley for the first time. His last appearance for Hibs came in April 1958, when he scored in a 2–1 win against Rangers.[4] Later that year he was finally given a testimonial match,[4] but was prevented from playing in it due to SFA regulations.[5]
Reilly won a total 38 caps for Scotland, scoring 22 goals.[3] He is Hibernian's most capped player and is fourth in the list of goalscorers for the Scotland national team. He also boasts an international strike rate of 61%, greater than that of Kenny Dalglish, Denis Law and Joe Jordan, and second only to that of Hughie Gallacher amongst those capped more than 15 times.[3] Late goals against Northern Ireland and England in the 1953 British Home Championship meant that Reilly earned the nickname of "Last-minute Reilly".[6] Reilly also scored 14 goals in as many appearances for the Scottish Football League XI.[7]
Reilly died in July 2013, aged 84.[8] In August 2019, his two Scottish league championship medals were sold at auction for £12,000.[8]