Abreu nabbed the June honor by batting .313 with 10 home runs, 22 RBIs and a .667 slugging percentage in 25 games.
He was given the rookie honor in the opening month of the season, in addition to winning the American League player of the month honor in March/April.
The 27-year-old native of Cuba became the first White Sox player to win rookie of the month twice in a season.
"First of all, I thank God and I'm very happy for the results," Abreu said through an interpreter on Wednesday. "I've just got to continue to work so we can continue to help the team get where we want to get."
Abreu entered play Wednesday tied for the major league lead in home runs with 26 and RBIs with 67. He leads all players with a .627 slugging percentage, as well as by hitting a home run every 10.73 at-bats.
"He's earned it," White Sox manager Robin Ventura said. "When you play well, you get recognized, and he deserves it. He's had a great month; he had a great month of April.
"It's just nice to see him get on a roll and have a nice month and get recognized for it."
Abreu is on pace to hit 50 home runs, which would break Albert Belle’s franchise record of 49, set in 1998. It also would break the major league rookie record of 49, set by Mark McGwire of the Oakland Athletics in 1987.
"I am satisfied with the way it's going, and I just thank God to allow me to do that right now," said Abreu, who entered Wednesday night’s game against the Los Angeles Angels on a 16-game hitting streak. "Things are going OK. I'm satisfied with it right now."
Despite his accolades this season, Abreu has always taken a team-first approach.
But there is another reason he seems so nonchalant about the honors he has received:
"First of all, I'm very grateful to Cuban baseball; but in Cuba, we don't have that many awards," Abreu said. "You never get that many awards. That’s probably why I look kind of cold when I get these awards here, because we're not used to that. That's just not part of the Cuban baseball."
The only time Abreu didn’t win the AL player of the month award was in May, when he missed 14 games with an ankle injury.