That means another team would have to give up a first- and a third-round pick to sign either free agent -- at least under the current collective bargaining agreement. But the players' situation could change depending on the outcome of the NFL's labor negotiations.
Linebacker Vernon Gholston, a 2008 first-round draft pick, also will be let go, the New York Daily News reported Monday.
Woody said on his Twitter account Monday that he had been informed of his release, and he thanked the Jets and their fans.
Woody, 33, just finished his third season with the Jets and his 12th in the NFL. He had arthroscopic surgery on his right knee in December.
Jenkins, acquired by the Jets in 2008, has missed most of the last two seasons because of major knee injuries.
"I had an absolute ball in New York," Jenkins said in an e-mail to The Associated Press. "I don't know what the future holds for my career as of yet, but I am in great spirits and still rehabbing to give it one more shot if possible. I just appreciated the opportunity I was given."
Taylor, who has 132.5 sacks in 15 NFL seasons, signed with the Jets before last season.
By parting ways with the four players, the Jets could save about $10 million.
The team also tendered wide receiver/kick returner Brad Smith (second-round level), quarterback Kellen Clemens (third round), safety Eric Smith (third round), cornerback Drew Coleman (sixth round), kicker Nick Folk (sixth round), offensive lineman Rob Turner (right of first refusal) and safety James Ihedigbo (right of first refusal).
The Jets acquired Cromartie (from the San Diego Chargers) and Holmes (from the Pittsburgh Steelers) in trades before the 2010 season. Cromartie tied for the team lead with three interceptions and added 42 tackles. Holmes' 52 receptions ranked third on the team, and his six touchdown receptions were second.
The Daily News also reported Tuesday that the Jets will bring back veteran running back LaDainian Tomlinson. The 31-year-old led the Jets in rushing (914 yards) and rushing touchdowns (six) last seasons after signing with New York as a free agent following nine years in San Diego.
The Associated Press contributed to this report.