The Cleveland Browns selected Johnson in the third round with the 77th overall pick in the 2015 NFL Draft. Johnson was the sixth running back drafted in 2015.
On June 16, 2015, the Cleveland Browns signed Johnson to a four-year, $3.10 million contract that includes a signing bonus of $710,092.
On August 1, 2015, Johnson injured his hamstring on the first day of the Browns' training camp. He was sidelined for the next ten days, and was inactive during the first preseason game against the Washington Redskins at FirstEnergy Stadium. During Johnson's first pre-season appearance, he was diagnosed with a concussion and was removed from the game. Throughout training camp, Johnson competed to be one of the primary running backs in the Browns' rotation against Isaiah Crowell, Terrance West, and Shaun Draughn. Head coach Mike Pettine named Johnson the backup running back, behind Isaiah Crowell, to begin the regular season. He replaced Terrance West after West showed up to training camp overweight and was released as part of final roster cuts.
He made his professional regular season debut and first career start in the Cleveland Browns' season-opener at the New York Jets and had seven carries for 22-yards in their 31–10 loss. On October 4, 2015, Johnson had eight carries for 31-yards and recorded a season-high nine receptions for 85-yards and scored his first career touchdown during a 30–27 loss at the San Diego Chargers in Week 4. Johnson scored his first career touchdown on a 34-yard pass by quarterback Josh McCown in the second quarter. In Week 14, he had a season-high 13 carries for 78 rushing yards in the Browns' 24–10 win against the San Francisco 49ers. He finished his rookie season in 2015 with 104 carries for 379 rushing yards and 61 receptions for 534 receiving yards and two touchdowns in 16 games and seven starts. Johnson's 61 receptions are the second-most by a Browns rookie, tied with wide receiver Greg Little. Among rookies, Johnson ranked first in receptions and receiving yards among rookie running backs and second in receptions overall, just under Oakland Raiders' Amari Cooper. Johnson was ranked sixth overall among rookies in receiving yards and was one of six rookies to surpass 500 yards receiving.