The USA international winger, formerly of Chicago Fire and PSV Eindhoven, was outstanding in yesterday's friendly victory over German minnows Gutersloh.
Gers No2 Ally McCoist said: "We were very pleased with DaMarcus Beasley. He is a great signing. He has not had a long time off, just about three weeks because he has played at international level. He is a great signing. He is very, very quick.
"In the season to come we will see a lot of great football by DaMarcus. Scottish football is very physical, but we also have a lot of physically strong players in our team, so DaMarcus can flourish."