The 19-year-old has signed a two-year deal with the Championship club, with the option of a further year, after turning down the offer of a new contract from Rovers.
Santos had been linked with a move to Premier League side Hull City.
"We are pleased to welcome Alefe to Derby County," head coach Steve McClaren told Derby's official website.
"He is a player with potential and has the determination to improve, so we are looking forward to working with him."
Santos made 27 appearances for Rovers in League Two last season.