Speaking at the BTIG charity event in New York, Johnson told reporters that the Jets are about to take off after selecting Darnold with the third overall pick of the 2018 NFL Draft.
"I honestly think (people) are going to look back 20 years from now and say this is the moment the Jets shifted into a new gear, that they became a great team," Johnson said.
The Jets haven't been so great of late. They posted back-to-back 5-11 seasons and haven't made the playoffs since consecutive trips to the AFC Championship Game following the 2009 and 2010 campaigns.
New York's desire for a top-tier quarterback was on display after the team made a blockbuster pre-draft trade with the Indianapolis Colts to move up three slots to No. 3. It paid a hefty price to do so as the Jets sent the No. 6 pick and a pair of second-round selections (Nos. 37 and 49) this year along with a second-round pick in the 2019 draft to the Colts.
From the team's perspective, the gamble paid off when Darnold, considered the top quarterback in the draft by NFLDraftScout senior analyst Rob Rang, fell to them at the third spot.
Darnold completed 303 of 480 passes for 4,143 yards, with 26 touchdowns and 13 interceptions with USC last season.
Now, Darnold is expected to compete with Josh McCown for the starting quarterback job.
The Jets were pleased with the performance of McCown last season, even though the 38-year-old compiled only a 5-8 record as a starter before sustaining a broken left hand in December that knocked him out for the rest of the season.
McCown completed 67.8 percent of his passes for 18 touchdowns, with nine interceptions.