The 24-year-old made an emotional acceptance speech after becoming the youngest MVP in eight years, BBC Sport reported.
The 2019 All-Star team captain averaged 27.7 points and 12.5 rebounds over 72 games, guiding his side to the Eastern Conference finals.
Antetokounmpo beat last year's winner James Harden to the award.
The 'Greek Freak' wept on stage as he paid a moving tribute to this late father Charles, who died in 2017.
"I want to thank my dad. Obviously, my dad is not here with me," he told the crowd in California.
"Two years ago, I had a goal in my head that I was going to be the best player in the league and do whatever it takes to help my team win, and I'm going to win everything.
"Every day I step on the floor, I always think of my dad and that motivates me and pushes me to play harder and move forward.
"Even when my body is sore, even when I don't feel like playing, I always show up and do the right thing."
"I want to thank my team, my teammates. MVP is not about stats and numbers. It is all about winning and all about making sure you go out there and do everything you can to win. I think that is what we did as a team."
Bucks general manager Jon Horst said, "We are beyond proud of Giannis for earning his first MVP award. This well-deserved honor is due to his relentless hard work and dedication in becoming the most impactful player in the NBA.
"Giannis propelled the Bucks to great heights last season with his leadership, drive and unselfish play. His grace on and off the court has made him one of the most admired players in the world."
Dallas Mavericks guard Luka Doncic, who averaged 21.2 points and 7.8 rebounds per game, won the Rookie of the Year Award.
Milwaukee Bucks' Mike Budenholzer was named Coach of the Year after leading his side to a 60-22 record, their best since the 1980-81 season.