Football was introduced to Bilbao by two distinct groups with British connections; British workers and Basque students returning from schools in Britain. In the late 19th century, Bilbao was a leading industrial town and attracted many migrant workers, including miners from the north-east of England, and shipyard workers from Southampton, Portsmouthand Sunderland. They brought with them the game of football, and came together to form Bilbao Football Club. Meanwhile, sons of the Basque educated classes went to Britain to complete their studies, developed an interest in football and on their return began to arrange games with British workers. In 1898, students founded the Athletic Club, using the English spelling.
In 1901, a meeting held in the Café García established more formal rules and regulations. In 1902, the two clubs formed a combined team, known as Bizcaya, in the first Copa del Rey and won the competition. This led to the eventual merger of the two clubs as Athletic Club in 1903. In the same year, Basque students also formed Athletic Club Madrid which later evolved into Atlético Madrid. The club itself declares 1898 as its foundation date, but others claim 1901 or 1903 as the true founding year.
Source: Wikipedia