The BBC said Millepied, 35, is to start the job in October 2014.
A former principal dancer with the New York City Ballet, he left in 2011 to create his own dance company in Los Angeles.
He and Portman began dating in 2009, married last year and have 1-year-old son together.
Portman won a best actress Oscar for her work in "Black Swan."
Celebrity Families of 2014 [PHOTOS]