Bojang was released by Doncaster Rovers at the end of last season and turned out for Posh as a triallist in a couple of pre-season friendlies.
Posh Academy director Kieran Scarff said: “Ethan came through the system at Doncaster. I knew him from my time at the club. He joined us right at the back end of last season and trained with us for a few weeks.
“At Doncaster, Ethan was always in the top two or three in his age group as he progressed through the ranks and it was a real surprise that he didn’t get a contract. Hopefully that will benefit us. He has an opportunity with us now.”
Bojang has been capped at Under 20 level by Gambia. The Under 23s start their season at Swansea on Monday (August 16).