The Jets also signed OLB Victor Ochi to their practice squad.
Should Davis clear waivers tomorrow, he would revert to the team’s injured reserve list.
McDougle, 25, is a former third-round pick of the Jets back in 2014. He was in the third year of his four-year, $2,863,876 contract when the Jets elected to cut him loose this past weekend.
In 2015, McDougle appeared in 14 games for the Jets and recorded six tackles, no interceptions and a pass defense.
Davis, 31, is a former fifth-round pick of the Bears back in 2008. He spent five years in Chicago before playing for multiple teams over the past three season including the Seahawks, Lions, and Jets.
In 2016, Davis has appeared in eight games for the Jets but has not recorded a single statistic.