The 34-year-old actress and 36-year-old Saturday Night Live head writer are yet to set a date after he popped the question.
Johansson’s publicist Marcel Pariseau told The Associated Press Sunday that the private couple is officially engaged after two years of dating, reports the publication.
It will be third time lucky for Johansson, 34, who was previously married to actor Ryan Reynolds and journalist Romain Dauriac.
She shares daughter Rose, five, with Dauriac. It will be the first marriage for Jost, who is the co-anchor of SNL’s Weekend Update.