A rep for the Hollywood actor told the publication: "The date was chosen to honour the birthday of the groom's late father."
Cage and his new wife exchanged traditional Catholic and Shinto vows.
And the National Treasure actor wore a Tom Ford tuxedo for the ceremony, while: "The bride wore a handmade Japanese Bridal Kimono from Kyoto that required three layers."
After they said their "I do's", they had a small reception with Cage's ex-wife, Alice Kim, and their 15-year-old son Kal-El present.
According to a state of Nevada marriage certificate obtained by DailyMail.com, Riko decided to take Nicolas' surname, while the document states that the couple applied for their wedding licence on January 10, which was the same day as the new Mrs Cage's 26th birthday.
Nicolas and Riko were first spotted together in February last year, and Cage confirmed their engagement in August.
He said at the time: "She left New York and went back to Kyoto, Japan, and I went back to Nevada and I haven't seen her for six months.
"We're really happy together and we're really excited to spend that time together so I finally just said 'Look, I wanna marry you' and we got engaged on FaceTime.
"I got her a black diamond engagement ring. Her favourite colour is black, so she wanted the black gold, and the black diamond. I customised and personalised it and I actually sent it to her by FedEx."
The marriage is Riko's first but the fifth for Nicolas, who was also previously wed to Patricia Arquette, Lisa Marie Presley, and Erika Koike.
His last marriage to Erika in March 2019 lasted just four days before the movie star – who also has 30-year-old son Weston with Christina Fulton – asked for an annulment when he claimed he was too intoxicated to understand what he was doing when the pair tied the knot.
The former couple were eventually granted a divorce in June 2019.