The couple had got engaged in October last year.
Hamilton had announced the news on Instagram where she posted a picture with the filmmaker sporting a sparkling, Monique Pean ring as Chazelle plants a kiss on her cheek.
The director, best known for films such as "Whiplash" and "La La Land", had referred to the actor as "the love of my life" while accepting the award for Best Director at the Critics Choice Awards in December 2016.
Hamilton, too, had appeared briefly in the multiple Oscar-winning films in a scene opposite Emma Stone as an annoyed cafe customer.
Chazelle was previously married to Jasmine McGlade, an executive producer on "La La Land". They parted ways in 2014.
The director is currently awaiting the release of "First Man", the biopic on Neil Armstrong which features Ryan Gosling and Claire Foy in the lead.
The film had its world premiere at the Venice Film Festival in August.