The Packers receive a conditional 2018 seventh-round pick in return for McCray.
McCray, 26, originally signed on with the Broncos as an undrafted free agent out of Florida back in April 2013. He spent the past three years in Denver before testing the open market this offseason.
The Packers signed him to a one-year, $800,000 contract back in April.
In 2015, McCray appeared in all games for the Broncos and recorded 15 tackles and a half sack. According to Pro Football Focus, McCray placed a total of 122 snaps last year.