The 20-year-old, who sealed the move late on Friday evening, has signed a four-and-a-half-year deal with the League One outfit, and manager Darren Ferguson is delighted to add the player to his squad at London Road.
The 41-year-old told the club's official website: "It is a really good signing. He is a young centre-half and I think that he is going to be a really top player.
"We have managed to get it done. Most of the Championship have been watching him and a Premier League club too, but we really like him."
Baldwin leaves Hartlepool having scored six goals in 85 appearances for the North-East side.