Rush, 26, went undrafted out of Central Michigan back in 2017. He later signed a three-year, $1.66 million contract with the Cowboys and managed to make the 53-man roster all three seasons.
Rush signed his $2.1 million restricted free agent offer after being tendered by the Cowboys this offseason. He was later waived and claimed by the Giants before agreeing to a restructured deal.
New York added Rush to their practice squad before releasing him a few weeks ago.
For his career, Rush has appeared in five games for the Cowboys, completing one of three pass attempts for two yards. He has also rushed for 13 yards.
Davis, 27, is a former fifth-round pick of the Packers back in 2016. Green Bay traded him to the Raiders back in September of last year for a sixth-round pick.
The Raiders waived Davis in December and he was later claimed off of waivers by the Dolphins. Daivs played out the final year of his four-year, $2.5 million contract.
He signed on with the Bears back in April but was cut loose last month.
In 2019, Davis appeared in 14 games for the Packers, Raiders and Dolphins and caught eight passes for 111 yards receiving and no touchdowns. He also rushed for 73 yards on four carries and a touchdown.
As a return specialist, Davis recorded 22 punt return attempts for 145 yards (6.6 YPR) and no touchdowns to go along with 23 kickoff returns for 506 yards (22 YPR) and no scores.