Middleton spent the past three seasons with the Jets. He has played 11 career games with four starts.
Middleton has 28 career tackles and four passes defensed. He also made five special teams stops.
Middleton originally entered the NFL as an undrafted college free agent with the Jets in 2016.
The Jets waived him out of the preseason, and he had been a free agent since.
Middleton has spent time on injured reserve twice for torn pectoral muscles.