Johnson spent several hours at the Jets' facility, took a physical and capped the day by attending the New York Knicks- Brooklyn Nets game in Brooklyn. The crowd cheered when his face appeared on the JumboTron.
Johnson's visit with the Jets went well, a source told ESPN.com's Rich Cimini, but there could be other teams interested. Ideally, the Jets would like to get a deal wrapped up by Monday, the start of the offseason program, but fiscally conservative general manager John Idzik won't overpay in a sluggish running-back market.
Tuesday's meeting marks Johnson's first visit since being cut by the Tennessee Titans on April 4.
Johnson, 29, is a three-time Pro Bowler who would add a legitimate speed threat to a Jets backfield that features the 222-pound Chris Ivory, who rushed for a career-high 833 yards last season.
Johnson was one of the league's most dynamic players early in his career. He ran for 2,006 yards in 2009 and is one of only six players to rush for at least 1,000 yards in his first six seasons, along with Barry Sanders, Curtis Martin, LaDainian Tomlinson, Eric Dickerson and Corey Dillon.
He was the 24th selection in the 2008 draft out of East Carolina.
After three seasons, when he ranked as one of the league's best values, Johnson sold himself to the Titans as a "playmaker" who shouldn't be constrained by the values placed on running backs. Following a training camp holdout in 2011, Johnson got a four-year, $54 million contract from Tennessee.
Information from ESPN NFL Insider Adam Schefter and ESPN.com Jets reporter Rich Cimini was used in this report.