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 James Bowman, which was named by BBC Music Magazine as one of the top 20 recordings of all time. more