The 19 year-old left the Hammers earlier this year in search of first-team football and went on trial at Southampton.
Corbett played twice for the West Ham Under 21 side in the EFL Trophy last season, including a substitute appearance in a 3-0 defeat at Posh. He scored the only goal in a 1-0 win at Portsmouth.
Posh have also confirmed the arrival of teenage forward Joe Taylor from National League King’s Lynn, a story that appeared on the Peterborough Telegraph yesterday.
Both players are expected to play initially for Posh under 23s. Taylor can’t play for the Posh first team until January, but Corbett can play immediately.
“We believe they are players we can improve,” Posh chairman Darragh MacAnthony said. “There is no pressure on either of them. They will play plenty of under 23 games and then hopefully get into the first yeam.”