The Pro Football Writers of America announced the trio's awards on Tuesday.
Mayfield was named the Rookie of the Year. Barkley received Offensive Rookie of the Year honors. Leonard was named the Defensive Rookie of the Year for his efforts.
The 2018 PFWA All-Rookie Team also included wide receivers Calvin Ridley and D.J. Moore, tight end Chris Herndon, center Billy Price, guards Will Hernandez and Quenton Nelson and tackles Mick McGlinchey and Braden Smith.
The PFWA's top rookie defenders also included: defensive linemen Bradley Chubb, Marcus Davenport, Da'Shawn Hand and Daron Payne; linebackers Roquan Smith and Leighton Vander Esch; cornerbacks Jaire Alexander and Denzel Ward; and safeties Jessie Bates and Derwin James.
Kicker Jason Sanders, punter Michael Dickson, kick return Tremon Smith, punt returner Christian Kirk and special teamer Zeke Turner also made the All-Rookie squad.
Mayfield, 23, completed 63.8 percent of his passes for 3,725 yards, 27 touchdowns and 14 interceptions in 14 games this season for the Browns. He posted a 6-7 record as a starter.
Barkley, 21, ran for 1,307 yards and 11 scores on 261 carries in 16 games this season. He also led the league with 2,028 yards from scrimmage, including his 721 receiving yards on 91 receptions.
Leonard, 23, led the league with 163 tackles and 111 solo takedowns. He also had eight passes defensed, four forced fumbles, two fumble recoveries and two interceptions in 15 starts.
While Mayfield and Barkley went No. 1 and No. 2 overall, respectively, in the 2018 NFL Draft, Leonard was drafted in the second round as the No. 36 overall pick.