The 20-year-old free agent joins on a one-year deal having shown enough during pre-season for O's manager Russell Slade to offer him a contract.
"Johnny has impressed me in the couple of performances he's put in for us," Slade told the club's official website.
"He's got good pedigree and a very strong left foot. I think we will see him play an ever-increasing part as the season goes on."
Gorman has made nine appearances for Northern Ireland during his short career and will come into contention for Orient's season opener away at Carlisle.