07 Vestur was established in its current form in November 2007, although its history can be traced back to the formation of a team called FS Vágar in December 1993. That club experienced a reboot in 2004 and as a result, some sources consider that to be the current team's date of formation. However, the club officially lists 2007 as its foundation and also references that year in its name. Throughout history, the team's various entities have struggled to establish themselves within the Faroe Islands as a consistent, top tier side.
FS Vágar was founded in 1993, after a merger between two previously existing teams, SÍF Sandavágur and MB Miðvágur. The intention was to bring a higher standard of football to the region and in 1995, the team gained promotion to the top flight. In 1998, SÍ Sørvágur also merged with the club. However, they were unable to retain their spot in the division. In 2004, the team disbanded, amidst mounting tensions between the three clubs which formed it. Later in the year, the club was re-founded as FS Vágar 2004, after pressure from supporters. Then, in 2007, they re-merged with SÍ Sørvágur to create 07 Vestur.
To date, 07 Vestur have struggled to remain in the Faroe Islands Premier League, having several one year long stints in the division, suffering relegation at the end of each one. They were crowned champions of the country's second tier in 2008, 2010 and 2012.
Torkil Nielsen is perhaps the side's most notable former talent. The former Faroe Islands international midfielder represented various incarnations of the club in the 1990s and 2000s and had previously played for SÍF Sandavágur.
07 Vestur's home matches are played at á Dungasandi. The venue has an artificial turf and is able to hold up to 2,000 people.