The orchestra said Davis died Sunday after a short illness.
One of the best-known figures in British music, Davis worked with the London symphony for more than half a century.
He first conducted for the LSO in 1959 and took the principal conductor post in 1995, serving until 2006 before becoming president.
The orchestra said Davis had been "at the head of the LSO family for many years."
Associated in particular with the works of Wolfgang Amadeus Mozart, Jean Sibelius and Hector Berlioz, Davis won three Grammy Awards -- two in 2002 for the LSO's recording of "Les Troyens" by Berlioz, and one for Giuseppe Verdi's "Falstaff" four years later -- and a host of other trophies.
Colin Rex Davis was born in the southern England town of Weybridge on Sept. 25, 1927, one of seven children of a bank clerk.
Thanks to a generous relative, he studied at the private school Christ's Hospital, then at the Royal College of Music, before spending his compulsory military service as a clarinetist with the band of the Household Cavalry.
Because he did not play piano he was denied a place in the music college's conducting class, and initially he struggled to find conducting work. But after filling in to acclaim for Otto Klemperer at the Royal Festival Hall in 1959, his career took off.
Apart from his work with the LSO, Davis spent periods as chief conductor of the BBC Symphony and music director of the Royal Opera House, and worked with ensembles around the world, including the New York Philharmonic, the Boston Symphony Orchestra and the Bavarian Radio Symphony Orchestra. He was knighted by Queen Elizabeth II in 1980.