Meade started his career at Arsenal as a schoolboy in 1977, and turning professional in 1980. He was the leading scorer for Arsenal's reserve side in the London Combination for both the 1980-81 and 1981-82, and made his first-team debut against Manchester City on October 17 1981. He went on to total 16 league appearances that season (eight as substitute), scoring four goals.
However, a cartilage injury ruled him out of most of the 1982-83 season, but on his return he scored twice against Brighton & Hove Albion in February 1983. He followed that up with a hat-trick against Watford and then a brace against Tottenham Hotspur in December that year. However, the signings of Paul Mariner and Charlie Nicholas meant Meade had been pushed down the pecking order at Arsenal, and he made only eight appearances in 1984-85. In total he made 51 appearances and scored 16 goals for Arsenal.
He was sold to Sporting Clube de Portugal in the summer of 1985, where he was a major part of epic Sporting 7-1 trashing of Benfica, in 14th December 1986, scoring 1 goal. He went on to have stints at Real Betis (on loan), Dundee United, Luton Town, Odense BK, Ipswich Town (on loan), Plymouth Argyle (on loan), Brighton, Hong Kong, Brighton and finally Crawley Town.