The 22-year-old has become the Rams’ first signing of the January transfer window and could make his debut in their FA Cup trip to West Brom on Saturday.
Midfielder de Sart has made just one appearance for Boro this season, having moved from Standard Liege last February.
“It’s not a big surprise for me (coming out on loan). I didn’t have a lot of game time with Middlesbrough and I want to play games,” he told Rams TV.
“When Derby County came (in for me), it was clear for me that this was my first choice. I didn’t want to hear any other offers, because I know that Derby is a good club and play good football. It was an easy choice for me.”
Boss Steve McClaren added: “He is a talented player with plenty of potential and, having made the move from Belgium, he has been in English football for almost a year now. I’m looking forward to working with him.”