The highly-rated duo were part of Town’s second-year scholars to depart Montgomery Waters Meadow this summer, while midfielder Josh Barlow agreed a new contract.
Wilson and Crompton are believed to have been offered short-term deals but opted to look for more secure offers elsewhere.
Talented Crompton attracting interest from clubs including newly-crowned Scottish champions Celtic who have tracked his progress.
Priorslee-based right full-back Wilson, 18, made two senior appearances last season and earned international honours with Northern Ireland’s under-18s, with whom he won a first cap and earned plaudits for his display.
He was previously part of the academy set-up at AFC Telford United and Derby County.
Crompton, 18, meanwhile, previously spent 10 years at Wolves and was extremely highly-regarded in the Town academy.
The rangy Crompton, who is also from Telford, arrived at the club a midfield player but has mostly operated at centre-half for Town’s youth side. He earned a reputation as one of the top performers in the age group and also trained with the first team, although did not make a senior matchday squad.
Both Wilson and Crompton were understood to be keen to remain at Shrewsbury to try to push further into the first-team picture.
They both endured difficulties with injury. Wilson spent a period of months on the sidelines before his EFL Trophy involvement while Crompton only returned from a back problem towards the end of the season.
Wilson, who made his senior debut in the Trophy win over Wolves Under-21s last October and also played 90 minutes in the competition at Wigan the following month, last week publicly confirmed his exit.
He tweeted: “Thank you to everyone at Shrewsbury Town for the last three years at the club. Excited for the next chapter.”
Former Cheltenham midfielder Barlow, 18, agreed his deal and will join fellow academy graduates Tom Bloxham – who was recently rewarded with a new and improved three-year contract – Charlie Caton and Jaden Bevan in Steve Cotterill’s first-team squad next season.