The 17-year-old, who can operate in central defence or midfield, has earned rave reviews in his first season at Victoria Park.
"His maturity is fantastic and the way he reads the game is excellent," manager Neale Cooper told the Hartlepool Mail. "For us to have him - a young kid from London - that's credit to what we try and bring in to the club.
"I've got such high hopes for the boy and hopefully he'll get better and better."
Baldwin only joined the club last summer from Faversham Town after a successful trial and made his first-team debut against Colchester in December before going on to make a further 16 appearances.
He is one of eight players aged 18 or under to have been handed first-team experience this season. The club have refused to comment on the length of Baldwin's new contract.