Scarlett Johansson and Colin Jost Are 'So Happy' and 'Madly in Love with' Baby Cosmo: Source

Scarlett Johansson and Colin Jost can't get enough of their baby boy.

The couple, who wed last October, now have a newborn on their hands, son Cosmo, and sources tell PEOPLE that Johansson and Jost are soaking in the new journey together.

"They are very private but elated over the baby," an entertainment source tells PEOPLE, adding, "They are both so happy and madly in love with the baby."

"They wanted this child who will fit right into their lives since they already have her daughter," the source adds of Rose Dorothy, whom the Sing 2 actress shares with ex-husband Romain Dauriac. "They are an awesome couple, both talented, smart and clever. They will be the best parents."

"Colin is considerate and helpful in everyday life so adding one more to the mix should be fine," the source adds. "The baby is the best thing ever for both of them."

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Additionally, a show business insider tells PEOPLE about Johansson and the Saturday Night Live star's parenting styles: "Each has a great sense of humor which will help with the added duties and stress of a newborn."

"His quick wit will help them through sleepless nights and any other issues that arise with a baby. Being able to laugh together is a great marital asset," the insider says. "Having great communication helps when this added layer of responsibility enters their lives. They are happy. And now is a good time to get used to their new lifestyle."

Last Wednesday, after PEOPLE confirmed that the pair welcomed their first baby together, Jost then gave more insight about their new family of four.

"Ok ok we had a baby. His name is Cosmo. We love him very much. Privacy would be greatly appreciated," he wrote on Instagram, then joking with his SNL costar Michael Che, "For all inquiries please contact our publicist @chethinks." He also added the hashtags: "#wegotawaywithitforalongtime" "#nokidspolicy" and "#weregoingtodisneyworld."

For more on Johansson and Jost's newly expanded family, pick up the new issue of PEOPLE, on newsstands nationwide Friday.