Johansson's publicist Marcel Pariseau confirmed the happy news to the Associated Press on Sunday.
The 4-time Golden Globe nominee is best known for her role of Natasha Romanov/Black Widow in the Marvel Cinematic Universe films. Black Widow is the only female hero among the six core Avengers. Jost recently appeared on the red carpet with his then-girlfriend for the release of "Avengers: Endgame."
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Jost is best known as the co-anchor on the "Weekend Update" segment on "Saturday Night Live." His fiancee is a member of the elite "Five-Timers Club," people who have hosted the sketch-comedy series at least five times.
The couple has been together for two years. Pariseau said they haven't yet set a wedding date.
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The Associated Press contributed to this report.