He started by describing his difficult year, including the details of his struggle with substance abuse and his split from ex-wife Anna Marie Tendler.
"I went to rehab in September, I got out in October. I moved out of my home from my ex-wife," he told Meyers.
After being in rehab for months, the Emmy-winner finally got together with Munn, 41, who he said he was very lucky to have met.
"She's kind of held my hand through that hell, and we're having a baby together," he eventually shared. The Saturday Night Live writer followed up by admitting that he was "nervous" leading up to the announcement.
"I'm gonna be a dad!" he gushed in the interview, adding, "We're both really, really happy."
Later in the clip, Mulaney told the television host that "Olivia and this baby have helped save me from myself and this early journey out of recovery."
Mulaney revealed in May that he and Tendler would be getting a divorce after six years of marriage.
"I am heartbroken that John has decided to end our marriage," Tendler told Page Six at the time. "I wish him support and success as he continues his recovery."
Mulaney was first linked to Munn, who previously dated NFL player Aaron Rogers, back in May, and the new flames have been seen heating up their romance all summer long.
In June, they were spotted having lunch together at Rick's Drive In & Out in Los Angeles, Calif.
"They were having a great time during lunch, laughing and talking," a source told PEOPLE at the time. "They were really enjoying each other's company."