The Scot made 265 appearances for United and scored 145 goals, including two in their 1963 FA Cup final win over Leicester - their first major trophy after the Munich air disaster in 1958.
He had netted for Arsenal in the last league match United played before the plane crash, which killed 23 on board.
Herd, who won five international caps, started his career at Stockport and also played for Stoke and Waterford.
The son of former Manchester City forward Alec Herd, he made his senior debut for Arsenal in 1954 and scored 99 goals in 166 appearances for the Gunners.
After joining United in 1961, he scored in his first appearances for the club in the FA Cup, League Cup and all three European club competitions, forming a formidable partnership with compatriot Denis Law.
He won the league title twice while at Old Trafford but was not selected for United's European Cup final victory over Benfica in 1968.
After retiring as a player, Herd was briefly manager at Lincoln City.
Former Manchester United and Arsenal striker David Herd has died aged 82.