"I just want to take a moment out of my day to invite you to the Marine Corps Ball on Nov. 18 in Greenville, North Carolina, with yours truly," Marine Sgt. Scott Moore says in the YouTube video, which has gotten over 2 million hits.
Moore said he posted the video after some Marines bet that he wouldn't make the video and post it.
"Of course, a bet between Marines must be honored, so I took the chance," Moore said in a statement.
Kunis heard about the video during an interview with Justin Timberlake on Fox News, and Timberlake convinced her to go.
Her publicist has not commented, but Moore said he heard from Kunis' staff.
Moore's parents talked to Robin Roberts on Wednesday on "Good Morning America."
"What hit me initially when I saw it, is boy, am I glad that he has a moment to take time to do something fun, because I know they put in extremely long hours and a lot of hard work," Moore's father said.