The team did not disclose terms of the deal, but earlier in the week multiple media outlets reported it is a one-year, $1.7 million contract.
Scott was drafted by Atlanta in the second round in 2012 from Virginia and averaged 7.1 points and 3.0 rebounds in 281 regular-season games spanning 4 1/2 seasons with the Hawks.
The 6-foot-8 Scott was limited to 18 games last season with the Hawks because of a knee injury, and he averaged 2.5 points and 2.1 rebounds in 2016-17. He was traded to the Phoenix Suns and was waived, last playing in a game on Feb. 15.
"Mike's toughness and ability to stretch the floor make him a good addition to our frontcourt reserves," Wizards president Ernie Grunfeld said in a statement. "His skill set fits in well with our offensive system and his tenacity fits in well with our overall team dynamic."
Scott's best season with the Hawks came in 2013-14 when he averaged a career-best 9.6 points and 3.6 rebounds. In 2015-16, he shot a career-best 39.2 percent from 3-point range.
Porter will receive $106 million for four years. The Nets and Porter had come to an agreement Wednesday on an offer sheet and the Wizards exercised their option to match.