It's a one-year contract for $2 million, according to a source. It has a maximum value of $3 million with incentives.
Siemian replaces Josh McCown, who spent the past two seasons with the Jets -- 2017 as the starter, 2018 as Darnold's backup. McCown, who will turn 40 on July 4, has been mulling his future. He recently indicated a desire to continue with his football career, but he wanted to spend time with his family before committing. If he decides to play, he could be a training-camp option for a team that needs an experienced backup.
Siemian, who posted a 13-11 starting record with the Denver Broncos, gives the Jets some experience behind Darnold, who started 13 games as a rookie. The only other quarterback on the roster is former New York Giants draft pick Davis Webb, who has yet to play in a regular-season game.
Siemian has no background with new coach Adam Gase or new offensive coordinator Dowell Loggains. Gase was the Broncos' offensive coordinator until 2014, the year before they drafted Siemian.
Siemian, 27, never saw the field for the Minnesota Vikings last season after the team acquired him in a trade with the Broncos, but he started 24 games from 2016-17 in Denver before suffering a subluxation in his left shoulder in December 2017, the same shoulder he had surgically repaired 12 months before that.
In Denver, Siemian threw 30 touchdowns and 24 interceptions with a 59.3 career completion percentage. The Broncos selected him in the seventh round (250th overall) of the 2015 draft.
The Vikings acquired Siemian a day before locking starter Kirk Cousins into a three-year, fully guaranteed deal during 2018 free agency.
ESPN's Courtney Cronin contributed to this report.