Cousin to the mother of Jack and Bobby Charlton, Milburn played two trial matches at St James' Park, as a 19-year-old in 1943. In the second of these, he scored six second half goals. Milburn made his competitive debut in the FA Cup in the 1945–46 season and was initially deployed on the left wing as a supplier to Charlie Wayman. However, Wayman was dropped before a 4–0 defeat to eventual winners Charlton Athletic in a 1947 FA Cup semi-final and when he afterwards vowed not to play for United again, manager George Martin made the decision to switch Milburn to cengtre forward. In his next match, on 18 October 1947, Milburn wore the number nine shirt for the first time and scored a hat-trick.
By the time Milburn left Newcastle in 1957, he had become the highest goalscorer in Newcastle United's history. He remained so until he was surpassed by Alan Shearer in February 2006. Milburn remains Newcastle's second highest goalscorer, having scored 200 competitive goals. Milburn's transfer to Linfield in 1957 was almost jeopardised when the Newcastle board demanded a substantial signing fee, and much to the anger of fans, Milburn was not immediately granted a testimonial. His signing for Linfield "added thousands to the gate" and he made 54 appearances, scoring 68 goals in four seasons in all competitions for the club. He was finally granted a testimonial ten years later, in 1967.
Milburn died of lung cancer on 9 October 1988, aged 64. His funeral took place on 13 October, and was attended by over 1,000 mourners at St Nicholas' Cathedral, in Newcastle. Tens of thousands of people lined the streets to watch the cortège pass. A statue of Milburn, costing £35,000 and paid for by donations received from Newcastle United supporters was erected on Newcastle's Northumberland Street before it was relocated in 1999 to St James' Boulevard and then moved again to its present position on Strawberry Place, just outside St James' Park.
In 2009, Goal.com listed Milburn as 43rd in their list of the top English players of all time.
