Mr Martelly, 50, has pledged to speed up earthquake reconstruction, develop the impoverished countryside and build a modern army.
The political novice was elected president in March in a run-off poll after a first round marred by fraud.
Hundreds of thousands of Haitians still live in tent cities after the devastating January 2010 earthquake.
Mr Martelly, known to Haitians as Sweet Micky, has been inaugurated in front of Haiti’s badly-damaged National Palace.
