The running back was announced as the recipient of the award Thursday. The winner is decided by an online vote by the public.
The Associated Press hands out its Rookie of the Year award at the NFL Honors awards show Saturday in Atlanta.
"Woke up to news that I won the 2018 Pepsi NFL Rookie of the Year Award," Barkley tweeted Thursday. "Now, how to I bring this back to NY?"
Barkley also posted a video on social media while walking with the trophy and his father through the streets of Atlanta.
"I just want to say thank you to everyone that voted for me," Barkley said. "I really appreciate it. I want to give a shoutout to my teammates also, that helped me get in the position I am in today. Also to the coaches and Pepsi."
New Orleans Saints running back Alvin Kamara and Dallas Cowboys quarterback Dak Prescott were the last two players to win Pepsi Rookie of the Year. Both players went on to win AP NFL Offensive Rookie of the Year honors.
Barkley led the NFL with 2,028 yards from scrimmage. He also had a rookie record 91 receptions in 2018. The No. 2 overall pick in the 2018 NFL Draft had 1,307 yards and 11 scores on 261 carries in his 16 starts this season.