The four-time NFL Most Valuable Player, who missed the 2011 season after neck surgery, was cut by Indianapolis on March 7 after a 14-year stint where he smashed the franchise's major passing records and won a Super Bowl.
NFL.com, citing an unnamed league source, said Manning told the Broncos on Monday he would sign with them.
The deal would end one of the most intense courtships ever for an NFL free agent with a flock of other teams including the Miami Dolphins, Washington Redskins, Seattle Seahawks among the clubs who openly expressed interest.
Manning had narrowed his choices to Denver, the Tennessee Titans and San Francisco 49ers and had worked out for all three teams and undergone physical exams.
In choosing the Broncos, the 11-time Pro Bowl quarterback and would remain in the American Football Conference (AFC), the same conference as the Colts, and join a team that won the AFC West division last season with an 8-8 record.
Indianapolis, who went 2-14 in Manning's absence, decided to rebuild rather than pay him a $28 million bonus he was due and own the top pick in next month's draft where quarterback Andrew Luck is pegged as the top choice.
Signing Manning, who turns 36 this month, would raise the prospects of Denver trading popular quarterback Tim Tebow, who led the team to several comeback wins last season and a first-round playoff victory over the Pittsburgh Steelers, but who struggled with his throwing accuracy.
Manning was wooed to Denver by Hall of Fame quarterback John Elway, the Broncos' head of football operations, who had said after the season that Tebow would enter training camp as the starting quarterback for the 2012 campaign.
Manning would be joining a team expected to be favourites in the AFC West over San Diego, Oakland and Kansas City.
The signal-caller may have felt a pull toward Tennessee, where he starred as a college player and where his wife is from, but even with Manning the Titans would have been considered a cut below the reigning AFC Central champion Houston Texans.
San Francisco, who feature a ferocious defence, was one win away from reaching the Super Bowl last season after falling in overtime to the New York Giants, led by his younger brother Eli Manning, in the National Football Conference title game.
But the competition in the NFC is not as familiar to Peyton, and the road to the Super Bowl could be more difficult with the Giants, Green Bay Packers and New Orleans Saints - winners of the last three Super Bowls - standing in the way.
Manning was cleared by his doctors to resume his playing career after going through a long waiting period for nerves in his neck to regenerate.
Workouts with the three finalists assured the bidders that he was on track to returning his Pro Bowl level.
Elway could put himself in Manning's shoes and appreciate what he could still accomplish late in his career.
The strong-armed Elway, a nine-time Pro Bowl quarterback, took Denver to three Super Bowls in four years from 1987, but did not win the championship until back-to-back Super wins in 1998-99, claiming his last one as a 38 year old before retiring.