After picking an offensive lineman earlier in the first round, the Atlanta Falcons traded back in to grab another big blocker.
In addition, the Rams sent their 203rd selection for Atlanta's second- and third-round picks (No. 45 and 79).
McGary joins Boston College guard Chris Lindstrom (No. 14) as rookies along Atlanta's offensive line.
"Got through a lot of adversity in his life," NFL Network draft analyst Daniel Jeremiah said of McGary. "He's a nasty finisher when you study him on tape. He's a little raw in pass blocking. He's very physical. They found something they wanted there with that physicality and toughness."