DiCaprio described himself as an "overly ambitious" child who had his heart set on becoming an actor, and it was his parents who "listened to a young child's dreams."
"And I could never be more thankful," he told Roberts.
DiCaprio, who won Best Actor in "The Revenant" after five Oscar nominations, told ABC on the red carpet before the ceremony that he's "particularly proud of this film."
DiCaprio said director Alejandro González Iñárritu achieved something "quite transcendent cinematically."
"I feel blessed to be able to do movies like this," he said. "I've worked for almost 25 years in this industry," he said, adding that "a lot of thought went into this movie."
"I think were all nervous right now," DiCaprio told Roberts, calling tonight "the culmination of so much effort on all of our parts."
"This is the big show," he said. "After years and years of hard work ... this is the end of it all."
DiCaprio then ended up walked off the stage with the coveted gold trophy. He previously scored Oscar nominations for his roles in "What’s Eating Gilbert Grape," "The Aviator," "Blood Diamond," and "The Wolf of Wall Street" but tonight was his first Best Actor win.