The Saturday Night Live star began dating the movie star in 2017 when Rose was just two years old. Jost admired Johansson's parenting skills during the five years they were together before welcoming their own son, Cosmo, now two. He expressed his admiration for Johansson as a mother, saying that getting to know Rose early on allowed him to see her in that role.

Johansson and Jost first met when she hosted SNL in 2006, long before she married Ryan Reynolds. They began dating more than a decade later. Johansson was briefly married to Reynolds before finding love again with a French journalist and art dealer, with whom she shares Rose. After Johansson's divorce in 2017, she and Jost reconnected and officially began dating.

Their relationship went public in 2017 after Johansson made a guest appearance on SNL. They confirmed their romance later that year at an event in New York City. They married in a small ceremony attended only by family and close friends during the COVID-19 pandemic in October 2020. They soon welcomed their first child, a son named Cosmo, in August 2021.

In an interview, the Weekend Update host shared that his wife likes to do normal activities, sometimes dressing up to keep a low profile. He has mentioned her talent for blending in when grocery shopping or participating in everyday tasks. The pair have also collaborated on a project, with him making a cameo appearance in Johansson's new film, Fly Me To The Moon, alongside Channing Tatum.

The actress has mentioned that the director brought him into the film because he is a fan of her husband. During a talk show appearance, Johansson humorously mentioned that Jost's cameo was part of their "prenuptial agreement" in which they support each other's projects. She also joked about his overly dramatic approach to helping her rehearse lines for her work, finding his intense performance amusing but not always helpful.