Reece was born in Cardiff and represented Wales at schoolboy level before being offered an apprenticeship at his hometown club Cardiff City. He made his way into the reserve side before spending a period on loan at Ton Pentre and was released by the club during the 1962-63 season and joined Pembroke Borough. During his time in Pembroke, Reece worked as a plumber whilst playing part-time. In 1963, NewportCounty managerBilly Lucas offered Reece another chance at professional football and, after just one season Somerton Park, his impressive displays convinced Sheffield United to pay £10,000 in April 1965 to sign him. Soon after he was called up to win his first cap for Wales against England. He settled quickly with the Blades, helping them to a ninth-place finish in the First Division during his first season but suffered a badly broken leg the following year which kept him out of the side for nearly a year. Despite this he went on to appear over 200 times for the club, establishing himself as a fan favourite with the Bramall Lane crowd. He returned to his hometown club Cardiff City in September 1972 alongside teammate Dave Powell in an exchange deal for Alan Warboys. Appointed club captain, he went on to play in a variety of different roles for the club and in his first two seasons his goals helped the club win the Welsh Cup, scoring a hat-trick in the second leg of the 1973 final and once in the second leg of the 1974 final. The club suffered relegation during the 1974–75 season, with Reece finishing as the club's top scorer with 8 goals, but managed to win promotion on the first time of asking the following year. Reece left the club at the end of the season and joined Swansea City where he spent a short time before retiring. After 1976 Reece played for non-League Barry Town.
After football
On retiring from his playing career he ran a family heating business before becoming a hotelier in Cardiff, running the Clare Court hotel in Grangetown. In April 2000, Reece was forced to have his right leg amputated after continually developing cysts behind his knee. He died in Cardiff, aged 61. He was also the brother of Welsh boxer Leonard "Luggie" Reece, and Grandfather of Welsh Rugby League International Lewis Reece.
