The highly-rated midfielder has signed a four-year contract after joining from the Terriers in a deal that sees Jacob Butterfield move in the opposite direction.
The 25-year-old was attracting interest from a host of clubs after winning Huddersfield's Player Of The Year award for last season, but Boro have won the race for his signature.
Clayton is a product of Manchester City's youth system, but he made his name at Leeds United, where he gained regular football and scored some explosive goals, including the club's Goal Of The Season in 2011/12.
He made 50 appearances for Leeds before moving across West Yorkshire, and in two years at Huddersfield he made 94 appearances, scoring 12 goals, and was a key figure in the club staving off relegation for two successive seasons.
Boro Head Coach Aitor Karanka said: "Adam is another player who will improve our squad and I'm delighted to welcome him to Boro. He is a strong player and a strong character and just the sort of person I want in my squad."
Clayton follows Kike, Emilio Nsue, Tomas Mejias, James Husband, and Kenneth Omeruo (loan) as the club's summer arrivals so far.