Washington, 25, is a former third-round pick of the Bills back in 2016. He was in the third year of his four-year, $3.189 million contract and set to make a base salary of $630,000 for the 2018 season when the Bills recently waived him.
Buffalo had been trying to trade Washington for a few years before they officially cut him loose. The Cowboys signed him to their practice squad last week.
In 2018, Washington has appeared in one game and recorded two tackles and no sacks for the Bills.