The little one, who was delivered via surrogate, is the first biological child for the couple and joins Lucas' adopted children 32-year-old Amanda, 25-year-old Katie and 20-year-old Jett.
The Star Wars creator and the Ariel Investments president wed in late June at Lucas' Skywalker Ranch in Marin County, Calif. It was the second marriage for Lucas and the first for the chairman of Dreamworks Animation.
Prior to taking the plunge, 44-year-old Hobson, who dated George for seven years before saying "I Do," opened up to Oprah Winfrey and shared what makes the pair's longtime relationship a success.
"I think it works because we are extraordinarily open-minded people and we're open to what the universe brings us," she said. "I think we didn't have preconceived ideas about what a partnership should be and so we allowed ourselves to discover something that was unexpected."
The newest edition to the family couldn't come at a better time for the 69-year-old filmmaker, who sold Lucasfilm to Disney for a whopping $4.05 billion in Oct. 2012. Star Trek directorJ.J. Abrams has since signed on to direct Stars Wars Episode VII, which is slated for release in summer 2015.