Henderson was born in
Glasgow in 1932, and started playing football as a youth with his
Bishopbriggs-based church team and for Kirkintilloch Boys Club. At first playing as a
centre forward, he also subsequently appeared at
inside forward and on the
left wing for the club. Unable to secure a first-team place, Henderson moved on to
Arsenal in October 1958 for £20,000, and made his debut against
West Bromwich Albion at
Highbury on 4 October; he scored twice in a thrilling 4–3 win. Injury interrupted his first season, but he still scored twelve times as Arsenal finished third in the league. He became a regular in the first team in the following two seasons. Swindin's tinkering with the Arsenal attacking line-up meant the versatile Henderson was unable to hold down any particular position in the side, and midway through the
1961–62 season he was transferred to
Fulham for £14,000. He had played 111 games for Arsenal in total, scoring 29 goals. In his first season at
Craven Cottage, Henderson helped Fulham reach the
1961–62 FA Cup semi-final, in which they lost narrowly to
Burnley. Henderson also helped keep the Cottagers in the First Division for two seasons. He was a Fulham regular up until March 1963, when he broke his leg. An attempted comeback was unsuccessful, and he left the club in 1964. He continued to play
non-league football with
Poole Town, where he was top scorer as they were promoted to the
Southern League Premier Division, and
Dorchester Town until his retirement from football in 1971. ==International career==