He joined the practice squad, while the Raiders activated quarterback Marcus Mariota off injured reserve.
Irving must still complete the NFL's new six-day player intake process.
Irving, 27, last played in the NFL in 2018. After being suspended by the league indefinitely for violating its policy and program for substances of abuse for the second time, he "quit" on an Instagram Live story last year in opposition to the NFL's drug stance, particularly in regard to marijuana.
The league reinstated him on Friday and Irving, perhaps buoyed by the thought of reuniting with Raiders defensive line coach Rod Marinelli, for whom he played in Dallas, began the COVID-19 testing process.
Still, while Irving will be eligible to enter the Raiders facility and sign his contract on Thursday, as long as his COVID tests remain negative, he is not expected to be added to Las Vegas' 53-man roster at that time. Nor will he play Sunday night against Tom Brady and the Tampa Bay Buccaneers at Allegiant Stadium.
Irving, a cannabis advocate, retweeted a statement last September that said he was being suspended for choosing "#plantsoverpills and was forced into a 3 month closed door rehab with a bunch of #opioid #addicts and only so I could go back to the league and be prescribed opioids."
The 6-foot-7, 290-pound Irving had 12.5 sacks in 37 games over four seasons for the Cowboys, including seven in eight games in 2017, but has played in only two games since the start of the 2018 season.
The Raiders, meanwhile, are coming off their bye week and could use help rushing the passer as their seven team sacks rank tied for 29th in the NFL, with defensive end Maxx Crosby leading Las Vegas with four sacks.
The Houston Chronicle first reported Irving would be signing with Las Vegas.