The former non-League defender joined up with the club on Monday and impressed enough during a training-match win over St Neots to prompt Posh boss Darren Ferguson to make his move.
The 18-year-old centre-back began his career at Dagenham and, after failing to make his mark there, also had spells at Dover Athletic and Thurrock before arriving at London Road.
'I like to think I can bring a physical side to the team, I am 6"5 and I still think I am growing," Santos told the club's official website.
"I am really pleased to be at Peterborough, I know a few of the lads already and the club is very ambitious. I am pleased to be here."
Ferguson went on to add: "He came to our attention through the Thurrock manager Mark Stimson, someone we have a good relationship with and he came in and trained with us on Monday.
"He played against St. Neots and did well.
"He is a great size, but he has good feet, looks after the ball fine.
"He is one for the future, but one that we know that a lot of clubs were looking at.
"Potentially, we feel he is a good signing for the football club."
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- Darren Ferguson
- Dover Athletic