The couple made the announcement through the Meals On Wheels charity, which said the wedding was attended by “immediate family and loved ones”.
The ceremony took place over the weekend and complied with coronavirus safety guidelines, the charity added.
Hollywood actress Johansson, 35, and Saturday Night Live star Jost, 38, got engaged in May 2019 after two years of dating.
Meals On Wheels said the couple’s wedding wish is to “help make a difference for vulnerable older adults during this difficult time” by donating to the charity.
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Avengers star Johansson has been married twice previously, to actor Ryan Reynolds and to journalist Romain Dauriac.
She and Dauriac have a daughter called Rose together, who was born in 2014.
This is Weekend Update co-host Jost’s first marriage. Speaking in October, two-time Oscar nominee Johansson said Jost’s engagement was like a “James Bond situation”.
She told Ellen DeGeneres: “He did, he killed it. It was a very James Bond situation. It was surprising.”