The 22-year-old moves to the Rams, having spent pre-season with Albion, following his move from Portsmouth this summer.
Graham Potter said, “We brought Matt to the club as a long-term prospect, and initially wanted him to spend pre-season here — and he has trained well and worked hard.
“Our plan was to make sure he would play regular senior football this coming season, and continue the excellent progress he’s made over recent seasons.
“This loan move to the Championship with Derby gives him a chance to play regularly in a competitive division, and is the next logical step for his own development.”
Clarke made the move along the south coast from Portsmouth in June and put pen to paper on a four-year deal to become the club’s first signing of the summer transfer window.
The defender enjoyed a successful 2018/19 season with Pompey and made a total of 54 appearances in all competitions, as the side won the EFL Trophy and reached the League One play-off semi-finals.