Miller was born and raised outside of Pittsburgh, Pennsylvania. His given name is "Ryan" but was called "Archie" at an early age because his personality was similar to Archie Bunker, the grouchy TV character.
Miller grew up in a basketball family. His older brother Sean Miller was a point guard who went on to play the position at Pitt and is currently the head coach of the Arizona Wildcats men's basketball team. Archie views Sean, who is 10 years older, as more of a mentor than a rival. Sean, then an assistant, recruited Archie to North Carolina State as a point guard. Sean also hired Archie as an assistant at Arizona when he got the job in 2009. “We didn’t grow up in the house together two years apart and the backyard,” Archie said. “... I basically look at him sort of as the role model, the guy whom to be like, the guy who to call when you need something, the one that helped you get to where you wanted to get to." Archie Miller's sister, Lisa, played Division I basketball at Toledo and Elon.
Both Archie and Sean played for their father, John Miller, a coach at Blackhawk High School, who went 657–280 in a 35-year coaching career, including 104–29 in the postseason, before retiring in 2005. He won eight Western Pennsylvania Interscholastic Athletic League championships, the second most in history, and four Pennsylvania Interscholastic Athletic Association titles. Miller noted how much he learned from his father, saying, "He's really teaching you how to be a coach, and you don't even realize it. He knew what hard work was. He knew what dedication was. He knew what preparation was. He knew how to communicate. It starts to come naturally to you. It's all you do. It's all you're around, and it's all you talk about.”
Following high school, Miller played point guard for North Carolina State from 1998 to 2002. As a senior, he helped lead the Wolfpack to the finals of the ACC championship game and was named to the all-tournament team. He finished his career there with an 84.6% free-throw percentage, a 42.9 three-point field goal percentage, and 218 three-pointers, which were all marks that ranked in the top 10 in school history. He graduated from NC State in 2002.
Miller spent time at several programs as an assistant coach, spending a season at Western Kentucky (2003–04), two at NC State (2004–2006), one at Arizona State (2006–07) under former coach Herb Sendek, two at Ohio State (2007–09) under Thad Matta, and two at Arizona (2009–11) under his brother Sean.
Miller became the head coach of the Dayton Flyers men's basketball team in 2011 and turned around a program that had back-to-back disappointing seasons. His first season with Dayton saw Miller take the school to 20 wins. His third year, in 2014, he had the Flyers in the Elite Eight with 26 wins and along the way Dayton upset three higher seeded teams. After the Elite Eight run in the 2014, Miller had to replace three starters and four seniors from that team. Despite having a depleted roster that featured just six players who were recruited to Dayton and no active player taller than 6-foot-6, Miller led his Flyers to a 27-9 overall record and to the third round of the 2015 NCAA tournament.
In the three seasons after the 2014 Elite Eight run, Miller averaged over 25 wins and each year the team made the NCAA tournament. The last two the Flyers earned the regular season Atlantic 10 title. The Flyers' 78 wins in from 2013-16 matched the best three-year period in school history. He was named a finalist for the 2015 Jim Phelan National Coach of the Year Award.
On March 27, 2017, Miller was named the 29th head coach in the history of the Indiana Hoosiers men's basketball team.
Miller employs a structured transition offense intended to open up games, create foul trouble for opponents, and score before the defense can get set. His offensive approach has been called "one of the most complete transition offensive systems you will find." He frequently uses a "Phoenix fast break" with players pushing the ball off of rebounds and turnovers in a flexible system that can take on a variety of alignments. He will modify the Phoenix break based on personnel to accommodate five guards or two post players on the floor at once. If an opponent scores, Miller employs a "Carolina transition offense" to create scoring opportunities which flow right into a motion offense.
The identity of Miller’s teams are rooted in defense. He employs a "pack line defense," which is a variation of man-to-man defense. Instead of the off-ball defenders pressuring their player and denying the pass, everyone except the player guarding the ball must be inside an imaginary line 16 feet from the rim. At all times a defender pressures the player with the basketball, while the other four defenders play in gap/help positions. However, if the offensive player picks up the dribble, all players go out and deny looking for the steal. The pack line defense is intended to discourage penetration, getting inside the paint, and forces opponents to win with a well executed offense and good outside shooting.
While attending NC State, Miller met Morgan Nicole (née Cruse), who was also a student and athlete for the Wolfpack. Morgan was on the NC State track and field team. The couple dated during college and tied the knot in 2003. Since then, they’ve had a daughter, Leah Grace.