Doctor Greenwood was born in Blackburn on 31st October, 1860. On 5th November 1875, two friends, John Lewis and Arthur Constantine, organized a meeting at the St Leger Hotel in Blackburn to discuss the possibility of establishing a football club in the town. Seventeen men attended the meeting and it was decided to establish the Blackburn Rovers Football Club.
Greenwood's older brothers, Thomas and Harry, joined the club. Thomas Greenwood was appointed captain and although Doctor was only 15, he also joined the club and by 1878 he was one of the stars of the side. Other players in the team included, Fred Hargreaves, Jack Hargreaves and Jimmy Brown.
In 1880 the club signed Hugh McIntyre, Fergie Suter and Jimmy Douglas from Scotland. This made them one of the best teams in England. Greenwood was recognised as being an outstanding full back and on 18th February 1882 he won his first international cap playing for England against Ireland. Also playing in that game were fellow Blackburn players, Jimmy Brown and Fred Hargreaves. England won the game 13-0. Greenwood's next game was against Scotland on 11th March, 1882. This time England team were beaten 5-1 and Greenwood was dropped for the next game against Wales.
In 1882, Blackburn became the first provincial team to reach the final of the FA Cup. Their opponents was Old Etonians who had reached the final on five previous occasions. However, Blackburn had gone through the season unbeaten and was expected to become the first northern team to win win the game. Doctor Greenwood was injured the team included five players who had won international caps, Jimmy Douglas, Fred Hargreaves, John Hargreaves, Hugh McIntyre and Jimmy Brown.
The Old Etonians scored after eight minutes and despite creating a great number of chances, Blackburn was unable to obtain an equalizer in the first-half. Early in the second-half George Avery was seriously injured and Blackburn Rovers was reduced to ten men. Despite good efforts by James Brown, Jack Hargreaves and John Duckworth, Rovers were unable to score.
Greenwood was an amateur player and stopped playing for Blackburn Rovers when it began to rely more and more on professional players.