Kópavogur Public Library was founded in the spring of 1953, then named Kópavogur Reading Society (Lestrarfélag Kópavogs). Poet Jón úr Vör was its first head Librarian.
For the first few years the Library was housed in Kópavogur Primary School (Kópavogsskóli) and later also in Kársnes Primary School (Kársnesskóli). In 1964 it moved to a 150 sq.m. area in Kópavogur Community Center and remained there until 1981 when it moved to its own premises at Fannborg.
The Library opened at its current premises, a new and elegant building on three floors, on the 11. of May in 2002.
In that same year Lindasafn, a branch from the Library was opened in Lindaskóli Primary School. Lindasafn is operated in collaboration with Lindaskóli Primary School Library on the second floor of the school's 190 sq.m. hall.