Davis, internationally renowned for his interpretations of Mozart, Sibelius and Berlioz, first conducted the LSO in 1959 and became its principal conductor from 1995 to 2006 after a fiery start to his career when he was known for his tantrums.
Over the years Davis mellowed as he worked with leading British musical institutions including the Royal Opera House and the BBC Symphony Orchestra while mentoring students at London's Royal Academy of Music and Guildhall School.
He also conducted extensively overseas, with the Boston Symphony Orchestra in 1972, as lead conductor of Munich's Bavarian Radio Symphony Orchestra 1983-1993 and as principal guest conductor of the New York Philharmonic from 1998-2003.
Davis died on Sunday after a short illness, and an LSO statement paid tribute to his "musicianship and his humanity".
Lennox Mackenzie, chairman and first violinist at the LSO where Davis was serving as president at the time of his death, described him as a master conductor who cared deeply about the musicians he led.
"He had a real understanding of great music and performed it with amazing energy, warmth, affection," Mackenzie told Reuters.
"He had no ego. He was not interested in self-aggrandizing or having his name in lights. All he cared about was music and all you wanted to do with him was play your best."
Antonio Pappano, music director at the Royal Opera House, described Davis as "a giant" and his death as a "huge blow".
"His passing represents an end of an era, where grit, toil, vision and energy were the defining elements of a leading international opera house," Pappano said in a statement.
"SMASHED" HIS LIFE UP
Messages of condolence flooded into the LSO's website and on Twitter from musicians who worked with Davis or were inspired by him -- even though the conductor himself admitted in interviews that he was not well liked in his early years.
He had a reputation for having a temper in the 1960s when he conducted many of the LSO's annual series at the Royal Festival Hall and was looked over as chief conductor for the LSO.
Later in life Davis said he faced a professional and personal crisis at that time. His first marriage collapsed and he married his family's au pair in 1964. She died in 2010.
"I decided that I didn't like anything in my life so I stood back and smashed it all up," he told an interviewer in 2002.
Mackenzie said Davis talked openly about his tempestuous past.
"He said he was hot headed, slightly arrogant and immature and when he thought about it now it made him shudder," he said.
In 1967 Davis was named chief conductor of the BBC Symphony Orchestra and became known on the international circuit. He still faced criticism though, enduring bad reviews and booing at the Royal Opera House in the 1970s.
However, in 1995 he was named principal conductor at the LSO where he won universal plaudits - a period of his career which Mackenzie described as Davis's "Indian summer". This time he ensured his ego remained in check.
"The less ego you have, the more influence you have as a conductor ... you can concentrate on the only things that really matter: the music and the people who are playing it," he told the Guardian newspaper in 2011.
Welsh soprano Katherine Jenkins was one of many fans who expressed sadness over the death of Davis, who shunned celebrity for his family and his hobby, knitting, which he said taught him patience. At one stage he had a pet iguana.
Davis received a long list of awards over his career for both his recordings and live performances included Grammys, two Classical Brit Male Artist of the Year awards and honours from Italy, France, Germany and Finland. He was knighted in 1980.
