Jacksonville had cut Mincey last week over repeated issues of tardiness and violation of team rules.
The 6-4, 265-pounder was drafted by the Patriots in 2006, and played under Jack Del Rio for 4.5 seasons with the Jaguars.
Wes Welker and Derek Wolfe have been ruled out for Thursday night's game against San Diego, while Champ Bailey is listed as questionable after having been limited during Wednesday's practice.
Trindon Holliday and C.J. Anderson were full participants and are listed as probable, along with 13 other Broncos, and all figure to be available.
Prater set a new NFL standard with a 64-yard field goal at the halftime gun, and added two more chip shots on the day.
It's the fifth such award for the eighth-year kicker, and the seventh weekly honor for Broncos players this season.
Yup, it's two days since the Broncos whipped the Titans, and they're already just two days from hosting the Chargers.
Such is the brutality of today's NFL.
Wes Welker and Derek Wolfe were the only players to miss practice on Monday, while Trindon Holliday was limited. 14 others were listed as full participants.
Matt Prater set a new NFL record with a 64-yarder at the halftime gun in Denver's Week 14 game against Tennessee.
Four players, including former Bronco Jason Elam, had held the previous record at 63 yards.
Citing his recovery from heart surgery and the desire to better communicate with his players, John Fox announced Friday that he would coach Sunday's game against Tennessee from the Denver sideline, rather than up in the coaches' booth.
As for the players, Derek Wolfe was ruled out, as expected, while Champ Bailey and Trindon Holliday are listed as questionable. This, despite Bailey having been a full practice participant on Thursday and Friday; Holliday made a limited return on Friday after having sat out Wednesday and Thursday.
Following an outdoor walkthrough, the Broncos' first practice since John Fox's return was forced indoors by cold and snowy weather.
Peyton Manning was held out for the fourth straight Wednesday; Derek Wolfe, Trindon Holliday, and Joel Dreessen also missed practice.
Wolfe is not expected to play Sunday, as doctors continue to try to figure out the cause of his frightening seizure-like episode.
Eric Decker's career day not only earned him a place in Denver's record book, it garnered him the AFC Offensive POW award for the first time.
The fourth-year wideout set a new personal best with 174 receiving yards in Denver's 35-28 win over Kansas City, and his four receiving touchdowns are the most by any player in franchise history.
Denver's route to the playoffs is actually a bit easier than had been reported earlier in the week. There are three scenarios that clinch a berth for the Broncos:
Kansas City Police have reportedly arrested two people in connection with a possible homicide that allegedly occurred in the parking lot at Arrowhead Stadium.
According to KCTV5, a man and his son arrived at their parked car during the game and found a third man going through the contents of the vehicle.