DeGrom won the award over Reds' outfielder Billy Hamilton and Cardinals second baseman Kolten Wong, while Abreu was chosen as the unanimous AL winner by the Baseball Writers' Association of America over finalists Dellin Betances of the Yankees and Matt Shoemaker of the Angels.
Hamilton finished second in the NL voting, while Shoemaker finished second in the AL.
DeGrom becomes the first Mets player to win the award since Dwight Gooden in 1984. The other Mets to be honored as NL Rookie of the Year are Darryl Strawberry (1983), Jon Matlack (1972) and Tom Seaver (1967).
DeGrom started the season 0-4, but went 9-2 with a 1.99 ERA in the last 15 starts of the season.
Cincinnati speedster Hamilton hit .250 with six home runs and 48 RBI. He was second in the National League with 56 stolen bases and led all NL center fielders with 10 outfield assists.
Wong hit .249 with 12 home runs, 42 RBI. He stole 20 bases.
Abreu is the sixth White Sox player to win the award and first since Ozzie Guillen in 1985. Ron Kittle (1983), Tommie Agee (1966), Gary Peters (1963) and Luis Aparicio (1956) are the other White Sox players to take home the award.
Abreu led all AL rookies in home runs, RBI, hits, doubles, runs scored and OPS. His 36 home runs were the most by an AL rookie since Mark McGwire hit 49 in 1987 on his way to winning the award that season.
Betances was selected as an All-Star and finished the season with a 1.40 ERA and 13.5 strikeouts per nine innings.
The 28-year-old Shoemaker picked up the slack after ace Garrett Richards was lost to a knee injury in late August. Shoemaker won seven of his last eight starts and finished the year 16-4 with a 3.04 ERA and 1.07 WHIP.
Tampa Bay Rays right fielder Wil Myers won the award last year.
- Scooby Axson