The 18 year-old Scotland international moves to Udinese for £4.75m, signing a deal to 2030.
Udinese say they have signed "one of the brightest young talents in European football".
Miller is the son of former Aberdeen midfielder Lee Miller and told the Well website: "Motherwell is all I've ever known. It's been my home since I was a young boy and I've achieved my dream of playing in the first-team, playing in the big stadiums and wearing the armband.
"My thanks goes to all the supporters for taking me in. For all the coaches I've worked under and who have helped me improve as a player and as a man, thank you. I simply wouldn't be here without their guidance and support.
"To all the players who I've played alongside with, and for all the kind words they've said about me, thank you. My team-mates have helped me through everything and allowed me to play with freedom.
"I want to also express my appreciation to all the staff behind the scenes at the club. Some are still there, some have moved on, but they all work so hard to keep the place going.
"This is a new chapter in my life and I move on filled with excitement. I may not be at Fir Park to cheer on the boys, but I'll be watching and following from afar. The club has a big place in my heart and I will always be grateful."