Wayne Brightly, who is due to appear in a Brooklyn court on May 12 to face charges of criminal coercion and falsifying information, paid Rubin Leitner $2 and sent him to meet investigators, still posing as the teacher, when the authorities closed in.
Mr Leitner has Asperger Syndrome and has spent years living on the streets.
New York's mayor and schools chief Michael Bloomberg has branded the scam "boneheaded", but red-faced New York education officials have been scrambling to explain how Mr Brightly was able to pass Mr Leitner off as himself. Mr Brightly, 38, is black and slim. Mr Leitner is 58, white and overweight.
Mr Brightly began teaching history 13 years ago before new requirements that staff pass a proficiency test in their subject were introduced in 2000. His temporary licence was due to expire last August. He persuaded Mr Leitner to step in for him, equipping him with a bogus ID.
The two met years earlier at Brooklyn college, where Mr Brightly received a bachelor's degree in 1992 and Mr Leitner was doing odd jobs, having gained a master's degree in history in 1979.
Daniel Schlachet, counsel to the special commissioner of investigations for New York's schools, described Mr Leitner as "unable to care for himself in any sense".
"At the same time he's highly functional in at least history," said Mr Schlachet, who likened Mr Leitner to the character played by Dustin Hoffman in the 1988 Hollywood movie Rain Man.