Dublin entered the championship as the defending champions, however, they were defeated by Meath in the Leinster final.
It was Galway's second consecutive final, having lost to Dublin in the previous year's decider.
The Tribesmen won their 5th All-Ireland title, beating Kerry by 5 points in the final, 0-15 to 0-10.
It was the start of the most successful era in Galway football, their "Three In A Row".
In 1964 only 2 Quarter-finals instead of the usual 4 were played in the Leinster football championship.