According to NFL Network's Ian Rapoport, the Davis deal is worth $5.5 million over two years with $3 million fully guaranteed in the first year.
Rapoport also reported that Mingo's contract is for one year, although he did not disclose any financial terms.
The 28-year-old journeyman is set to enter his seventh NFL season in 2021.
After getting selected in the fourth round of the 2015 NFL draft, the former South Carolina standout bounced around between several teams.
Davis didn't get much run during his first five seasons aside from the 2018 campaign in Seattle when he rushed for 514 yards and four touchdowns on 112 carries to go along with 34 receptions for 214 yards and one score.
He eclipsed those totals in 2020 as the fill-in starter for Christian McCaffrey, who missed all but three games because of various injuries.
In 15 contests, including 12 starts, Davis rushed for 642 yards and six touchdowns on 165 carries, while also catching 59 passes for 373 yards and two scores.
The Falcons' 2020 starter at running back, Todd Gurley, is a free agent, as is backup Brian Hill. That left Ito Smith and Qadree Ollison as the top running backs on the roster before Davis' signing.
Smith has rushed for just 689 yards and six touchdowns in three seasons, while Ollison has rushed for 53 yards and four touchdowns in two years, meaning Davis may be the favorite to start if Atlanta doesn't add any more backs.
As for Mingo, he adds some much-needed linebacker depth and gives the Falcons a quality special teams contributor.
Mingo was the No. 6 overall pick in the 2013 NFL draft by the Cleveland Browns after a standout collegiate career at LSU, and while he has not come close to living up to expectations, he has carved out a long NFL career.
The 30-year-old veteran is about to play for his seventh team in the past seven seasons, as he played three years for the Browns before playing one season each for the New England Patriots, Indianapolis Colts, Seattle Seahawks, Houston Texans and Bears.
Mingo, who won a Super Bowl with the Pats, has recorded 255 tackles, 12.5 sacks and five forced fumbles in 126 career games, including 40 starts.
He started three of the 16 games he appeared in for Chicago last season, finishing with 35 tackles and 2.5 sacks.
Mingo will lend support to linebackers Deion Jones, Foyesade Oluokun, Brandon Copeland and Co. for a Falcons defense that ranked 29th in total defense and 19th in scoring defense last season.