EB / Streymur was founded in 1993 in Streymnes, after two previously existing clubs, Eiðis Bóltfelag and Streymur, decided to unite. The decision was made in an effort to create a stronger team, which would be able to compete more strongly within Faroese football. Since the merger, the team have gone on to enjoy huge levels of success, firmly establishing themselves as one of the top sides in the country. Over recent years, they have established a strong rivalry with Víkingur, which is now their main derby match.
Previously, both Eiðis Bóltfelag and Streymur had been modest clubs, who had primarily competed in the second and third tiers of the league system. The merger created a far better base to build from and the club was able to gain promotion to the Faroe Islands Premier League in 1999-00.
It took little time for EB / Streymur to establish themselves in the top flight and in 2006, the club came close to winning the league, missing out on the title on the last day of the season. The following year saw them finish as runners up once again, although they were able to lift the Faroe Islands Cup for the first time. Using that success as a platform, they pushed on in 2008 and were able to win the league title and Faroe Islands Cup, completing a domestic double. Additional cup wins followed in 2010 and 2011, before the team were crowned as league champions for the second time in 2012. Their domestic success has seen the club enter the qualifying rounds of the UEFA Champions League.
Amongst the most notable players to have played for the side are Arnbjørn Hansen, Marni Djurhuus, Jón Sigurd Gleðisheygg, Hans Pauli Samuelsen and Sonni L. Petersen.
EB / Streymur play their home matches at Við Margáir. The venue is currently able to hold 2,000 supporters.