The Wales international midfielder joins Neil Warnock’s Championship side on a three-year deal for an undisclosed club-record selling fee, believed to be £3.5m, with an initial payment of £2.1m.
In his three years at the club Vaulks made 137 appearances and scored 17 goals.
He also won the 2019 EFL Community Player of the Year award, two club Community Player of the Year awards and the 2017/18 Player of the Year award.
Millers manager Paul Warne said: “Will leaves Rotherham United having made a huge contribution both on and off the field.
“He has become a very popular figure at the club and within the local community. He has epitomised everything about how I wanted Rotherham United to play during my time as manager, and has been a joy to coach.
“He has given me 100% week in, week out and thoroughly deserves his opportunity to play in The Championship. His rise from non-league to where he is today says everything about the guy and his desire to succeed. He is a shining example to any young pro. His day-to-day attitude has been first class, and we wish him all the best at Cardiff where I’m sure he’ll be a huge success under Neil and his staff.”