Irving was suspended indefinitely in March 2019 after repeated violations of the league's substance-abuse policy. He had also been suspended in each of the previous two years.
The 27-year-old is now an unrestricted free agent and can sign with any team.
"I am very proud of David and his commitment to self-growth," Irving's lawyer, Daniel Moskowitz, said Friday, per Aaron Wilson of the Houston Chronicle. "This is a story of redemption."
Irving last played an NFL game in October 2018 before suspensions derailed his career. He indicated he was done with the league in 2019, saying he "quit" in a social media video (warning: NSFW language):
He has now worked his way back to the NFL and will have a chance to restart a once-promising career.
The former undrafted free agent out of Iowa appeared in 27 games for the Cowboys in his first two seasons in 2015-16, eventually becoming a starter in his third year. He had seven sacks in just eight games in 2017, adding 22 tackles and a forced fumble.
Irving had just two appearances during the 2018 campaign, tallying one sack.