The exhibition is a study of the Renaissance artist's life from his earliest pen drawings to the late.
It reunites material not seen together since the posthumous dispersal of works from Michelangelo's studio in 1564.
The works on display come from collections in the British Museum, the Ashmolean Museum in Oxford and the Teyler Museum in Holland.
A collection of thumbnail sketches and red chalk studies traces the evolution of the painting of the Sistine Chapel in the Vatican, the AP reports.
Visitors are also shown drawings which Michelangelo used to tutor his students, alongside the pupils' own sketches.
The exhibition took a record 11,000 bookings before it even opened, beating the previous record of 3,670 advance bookings set by an exhibition of Persian art.
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