Crowley has penned a two-year contract, with a year's option.
Born in Coventry, the former England Under-19 and Ireland Under-17 international began his footballing career in the West Midlands as youth player with Aston Villa.
As a 15-year-old he was a key member of their Under-19s side which defeated Chelsea 2-0 in the final of the NextGen Series.
His displays brought him to the attention of London giants Arsenal who signed him up in 2014.
During his three-year spell with the Gunners, Crowley was loaned out on three separate occasions in order to gain first team experience.
Having turned out for Barnsley and Oxford United in the lower English leagues, he then joined Dutch outfit Go Ahead Eagles where he enjoyed a successful loan spell during the second half of the 2016/17 campaign.
Later that summer he joined fellow Dutch Eredivisie side Willem II on a three-year contract.
Having made 10 appearances for Willem II he gained further loan experience with Dutch club SC Cambuur.
After impressing with the second tier Dutch side, he returned to Willem II, where last season he starred and made 35 league and cup appearances, scoring five goals.
He also helped his side to the final of the KNVB Cup where they lost out to double winners Ajax 4-0 at Stadion Feijenoord.
Style-wise, the creative Crowley has tended to be used as an attacking midfielder, often playing in the number 10 role.
An accomplished passer of the ball, the 21-year-old has quick feet, is agile and can escape from tight situations and is also a set-piece taker who chips in with goals.
Crowley's form this season had brought him close attention from several clubs, including Feyenoord and PSV.
Crowley has outlined his desire to play for Ireland, and Mick McCarthy was present to watch him in the KNVB Cup Final. He has played at Under-17s level for the boys in green.
He is eligible for Ireland thanks to his grandparents, who are from Cork and Waterford.
Crowley becomes Blues' second summer signing for the senior side, after the permanent transfer of Gary Gardner.