In his acceptance speech, the 44-year-old Les Miserables star thanked his wife of 16 years, Deborra-Lee Furness, for the "sacrifices" she made for his career.
"None of this would have been possible and certainly none of it would have been as rewarding or meaningful to me, if not for my family," he said.
"I don't drag them along to too many things but I wanted them to be here today because I wanted to publicly say to them I understand that you guys do make sacrifices in order for me to be able to do what I do, and I want you to know that I appreciate it, and I want you to know that I love you with all my heart."
Hugh and Deborra-Lee are parents to son Oscar, 12, and seven-year-old daughter Ava.
The actor, who's been nominated for a Golden Globe and SAG Award for his role as Jean Valjean in Les Miserables, was joined at the ceremony by castmates Anne Hathaway and Amanda Seyfried, as well as the film's director Tom Hooper.