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The 22-year-old has taken just 35 appearances to set a new Premier League record of 36 goals in a single season to help Manchester City retain the title.
"I am honoured to have become the first player to win both awards in the same season – thank you to everyone who voted for me," said Haaland in a City statement.
"It has been an incredible first season in the Premier League and lifting the trophy last weekend in front of our fans at the Etihad was a very special moment for me."
The Norwegian, who was also named the football writers' player of the year this week, has scored 52 goals in all competitions as City close in on a treble.
Pep Guardiola's men face Manchester United in the FA Cup final and Inter Milan in the Champions League final next month.
"These awards would not have been possible without my amazing teammates, the manager and all of the staff at the club who help me perform on the pitch," added Haaland.
"Now we have two more finals to go and we want to finish the season strong."