Gase signed a three-year contract, according to a source.
Gase, 36, spent the day Wednesday interviewing with general manager Ryan Pace and head coach John Fox along with chairman George McCaskey and team president Ted Phillips. The interview marked the second time Gase spoke with the organization's decision makers. Gase interviewed with McCaskey, Phillips and consultant Ernie Accorsi during Denver's postseason bye week, just after the conclusion of the regular season.
A source told ESPN that St. Louis and San Francisco made efforts Tuesday night and Wednesday morning to bring in Gase before he flew to Chicago, including a Tuesday night phone call from Rams coach Jeff Fisher.
Gase worked the last six years with Fox on Denver's staff, spending the last two seasons as the team's offensive coordinator. The Broncos led the NFL in scoring offense (34 points per game), total offense (430.1 yards per game) and passing offense (315.8-yard average). The unit also racked up 157 plays for gains of 20 yards or more, which ranked No. 2 in the NFL.
In 2013, the Broncos set an NFL record by scoring 606 points, including a league-record 76 touchdowns. In 2014, the Broncos finished second in the NFL in scoring (482), which also ranked as the 25th-most in NFL history. The Broncos also accumulated 6,446 net yards, good fourth in the NFL.
One source told ESPNChicago.com's Jeff Dickerson that while Fox and Gase "have a strong mutual respect for one another," they have differing views on offense. While Fox prefers a more traditional ground attack, mixing in impact plays down the field when available, Gase is described as a "cutting edge offensive mind" who places of higher emphasis on passing the ball.
Gase has recently had the luxury of having his offense run by one of the greatest quarterbacks in NFL history in Peyton Manning. Now he is tasked with producing similar results with the enigmatic Jay Cutler at the helm. With Gase calling plays, the Broncos won 25 regular-season games, two straight division titles, and earned a berth in Super Bowl XLVIII.
Seven Broncos offensive players received Pro Bowl recognition over the last two seasons in running back C.J. Anderson, offensive tackle Ryan Clady, Manning, receivers Emmanuel Sanders and Demaryius Thomas along with tight end Julius Thomas and guard Louis Vasquez.
Gase spent the 2011 and 2012 seasons working with Denver's quarterbacks. During that span, Denver's passing offense ranked fifth in the NFL as the club finished second in scoring (30.1 points per game) and fourth in total offense (397.9 yards per game). Gase tutored quarterbacks Kyle Orton and Tim Tebow in 2011, and with the latter under center, the Broncos won the AFC West title and a Wild Card playoff game.
Orton and Tebow combined for 20 touchdown passes, as the latter set a franchise record for rushing yards by a quarterback (660).
Gase originally joined Denver's staff as receivers coach in 2009 and spent two seasons in that position, where he helped current Bears receiver Brandon Marshall earn one of his five Pro Bowl nods (2009).
Gase has also spent time with the 49ers and Detroit Lions.
Rams reporter Nick Wagoner and ESPNChicago.com's Jeff Dickerson contributed to this report.