He died at his home in Cambridge following an illness lasting several months, a statement on his website said.
It added his funeral will be private, with a memorial service to be held at a later date.
Hogwood worked with many leading orchestras around the world and was considered one of the most influential exponents of the early-music movement.
The conductor founded the Academy of Ancient Music (AAM) in 1973 and directed the academy across six continents for some 30 years.
The AAM also made more than 200 CDs, including the first-ever complete cycle of Mozart symphonies on period instruments.
Among his most famous recordings include the 1980 version of Handel’s Messiah with Emma Kirkby and Carolyn Watkinson, which was named by BBC Music Magazine as one of the top 20 recordings of all time.
Hogwood studied keyboard at Cambridge University with Rafael Puyana and Mary Potts and later with Zuzana Ruzickova and Gustav Leonhardt.
His first positions were as a keyboard player and musicologist with the Academy of Saint Martin-in-the-Fields under Sir Neville Marriner, and was a founder member of the Early Music Consort of London.
He was the artistic director of the King’s Lynn Festival and Boston’s Handel and Haydn Society. He was also a tutor at Harvard University, honorary professor of music at the University of Cambridge and a professor-at-large at Cornell University in the US.
“Christopher had extraordinary generosity of spirit,” Christopher Purvis, honorary president of the AAM, said.
“He was a great ambassador for historically informed music, the movement of which he was a founder. And he was happy to see the orchestra he founded develop and grow after he stepped down as director.”
The AAM’s music director Richard Egarr added: “I am deeply saddened by the news of Christopher’s passing. Christopher provided a fantastic legacy for me to build upon when I joined in 2006 and I know he will be greatly missed by all who knew and worked with him.”
Speaking to Sean Rafferty on Radio 3’s In Tune, soprano Dame Emma Kirkby said: “Some of the best players that now lead orchestras all over the world, they started with him.
“Chris was a natural academic, an incredibly clever man. He had an amazing capacity to absorb information of all kinds and a really sure sense of how things would be if he really tried to reproduce conditions… a very genial person.”
David Thomas from Trinity Laban Conservatoire of Music and Dance, London added: “He always said I want the music to speak for itself because it can, it’s good enough, it will… a very pleasant and lovely man.”