The actor began dating Moffett - real-life daughter of Fifth Doctor Peter Davison - back in 2008 and he proposed to her last Christmas.
The pair will apparently tie the knot later today in an intimate New Year's Eve ceremony in London.
"David and Georgia can't wait to get married, they are madly in love," a friend told the Daily Mail.
"They have tried to keep everything quiet and the wedding is for family and closest friends only."
The couple, who met when Moffett had a guest role in a 2008 episode of Doctor Who, welcomed their daughter in April. Moffett already has a 9-year-old son called Tyler.
Davison previously said of the pair's wedding plans: "I very much doubt they'll have a Doctor Who-themed wedding... I don't think that's their thing."