Undergaro proposed to Menounos on Wednesday during the star's appearance on Howard Stern's SiriusXM radio show.
The Howard Stern Show; Inset: Slaven Vlasic / Getty
"Although I said that this isn't a proposal, I want to ask you something," Undergaro asked the bride-to-be before getting down on one knee. "Will you make me the happiest man on Earth?"
After her initial disbelief, Menounos was reassured by the filmmaker, who promised, "It's not a joke," according to E! News.
"This I wouldn't joke about," he said. "I love you so much and this show's meant so much to both of us. … Why not make it official now? Will you honey? Will you accept?"
After putting on the ring (which Stern's co-host Robin Quivers described as "big"), Menounos' parents Costas and Litsa Menounos entered the studio.
Menounos and Underago have been dating since April 1998, and regularly work together on their joint AfterBuzz TV online network.