He visited with team officials at the team's Dove Valley complex near Denver Tuesday, and came to terms within a day.
Plummer, the starting quarterback for Arizona the last six seasons, inked a multi-year contract.
Terms were not disclosed, but he reportedly received a seven-year deal worth more than $40 million.
Team officials had been excited about his possible signing. They also wre hopeful about coming to terms with defensive tackle Darryl Gardner, who reached an agreement Wednesday afternoon.
Both players had been on Denver's wish list.
A press release issued by the team indicated that Plummer will sign his new deal Thursday.
General Manager Ted Sundquist already had made his feeling known.
"Obviously, we've done extensive evaluations on both these players," said Sundquist of both Plummer and Gardner. "We feel like they would be excellent fits for what we need on both offense and defense. We've had these guys singled out since a couple of weeks ago."
The signing of Plummer spells the end of Brian Griese's days in Denver. He had been shopping the entire offseason.
"Since John Elway retired, we really have fallen off where we move in the pocket and get away from the rush and make plays, plays that are not scheduled, not designed," Assistant Coach Alex Gibbs told a radio station in Phoenix this week. "Brian Griese was not as good in that."
Shanahan targeted Plummer after giving Griese permission to seek his own trade. Two years ago, Shanahan had given Griese a six-year, $39 million contract.
Off-the-field problems related to drunk driving incidents and poor leadership skills didn't help Griese, who was a loner in the locker room.
Plummer, 6-2, 212-pounds, has completed 1,540-of-2,754 passes for 17,622 yards, with 90 touchdowns and 114 interceptions in 84 NFL games, including 82 starts. He was the fastest Cardinal player to reach 10,000 career passing yards. He also has rushed for 1,183 yards on 247 attempts, with 10 scores, including four in 1998, the most by a Cardinal quarterback in over 20 years.
Plummer, 28, also had been heavily courted by the Chicago Bears. He has an uncanny ability to produce in last-minute situations, and led the Cardinals to 21 come-from-behind victories. In 1998, his first full season as a starter, he guided the Cardinals to their first playoff appearance since 1982, and their first post he season victory since 1947.
After suffering through frustrating 1999 and 2000 seasons that were impacted by injuries, he rebounded in 2001 and did not miss an offensive play. He started all 16 games last year, when he equaled a career-high with 18 touchdown passes.
Drafted by Arizona in the second round of the 1997 NFL Draft out of Arizona State, 42nd overall, Plummer started 40 consecutive games at quarterback in four years for the Sun Devils. While at Arizona State, he set career records for completions (632), pass attempts (1,142), passing yards (8,827), and touchdown passes (65).
As a senior, he was a consensus All-America selection and unanimous Pac-10 Offensive Player of the Year after leading his team to an undefeated 1996 regular season and a Rose Bowl appearance. In addition, Plummer finished third in the Heisman Trophy balloting, the highest finish for a Pac-10 player since Washington defensive tackle Steve Emtman placed fourth in 1991.
Meanwhile, Gardener was considered the premier defensive tackle on the open market. He played for Washington last season.
After recovering from back surgery in 2001, Gardener started 15 games last season, recording 71 tackles, four sacks, and one fumble recovery.
In Denver, he will replace veteran Chester McGlockton, who was released last week in a salary cap move.
Gardener, a 1996 sixth-round pick by Miami out of Baylor, played his first six NFL seasons with the Dolphins. The 6-6, 295-pound native of Baltimore is a solid run stopper, has registered 393 tackles, and has 93 1/2 sacks in 97 career games.