Davis first served as conductor of the orchestra in 1959 and became its principal conductor in 1995. He held the position until 2006 when he was appointed president.
"He will be remembered with huge affection and admiration by the LSO and our thoughts are with his family at this time," the orchestra said in a statement on its website after Davis died Sunday night.
"Sir Colin's role in British musical life was immense. Alongside his commitment to the LSO, he forged special relationships with the Royal Opera House, the BBCSO, and the English Chamber Orchestra, as well as mentoring many young performers and conductors at the Royal Academy of Music and the Guildhall School," the LSO said in its statement.
"He was internationally renowned for his interpretations of Mozart, Sibelius and Berlioz, and music lovers across the world have been inspired by his performances and recordings. His musicianship and his humanity have been cherished by musicians and audiences alike."