Vernon, 28, told reporters that Cleveland's busy offseason sets them up for a possible playoff berth this season. The Browns acquired Vernon and All-Pro wide receiver Odell Beckham Jr. in March from the New York Giants.
"It's been a lot of rough years for the Browns, so it can only last so long," Vernon said, according to the Akron Beacon-Journal. "The plan is set up. We've just got to execute it."
Vernon made his first Pro Bowl last season. He had seven sacks in 11 games.
The Giants traded Vernon for offensive lineman Kevin Zeitler on March 8. Vernon was later added to the Beckham trade when the league year began March 13.
Vernon is expected to compliment edge rusher Myles Garrett on the defensive line.
"They say you're going to get what you play for, so you're going to get what you traded for, and I'm glad to be here," Vernon said.
Cleveland went 7-8-1 last year after going 1-31 from 2016 to 2017.