Gordon was signed to the practice squad of the Kansas City Chiefs on Monday, he told ESPN's Jeremy Fowler.
The Chiefs and Broncos meet twice this season, in Week 14 in Denver and Week 17 in Kansas City.
Gordon, 29, is a two-time Pro Bowler in his eighth NFL season. He played five seasons for the Chargers and the last 2½ with the Broncos. He has rushed for 6,462 yards and 55 touchdowns and caught 309 passes with 14 touchdowns over his career, with his best year in 2017 with the Chargers.
This season, he rushed for 318 yards and caught 25 passes in 10 games. But he fumbled five times and the Broncos released him after his final one in Week 11 against the Raiders.
Rookie Isiah Pacheco leads the Chiefs with 455 rushing yards. Another running back, Jerick McKinnon, is fourth on the team with 29 catches. Ronald Jones made his season debut for the Chiefs in Sunday's win over the Rams and caught one pass for 22 yards while rushing four times for 12 yards.
Clyde Edwards-Helaire, who began the season as the starting running back, is on the injured reserve list with a high ankle sprain but had lost much of his playing time to Pacheco before the injury.