The League One club have also signed Norwich City midfielder Ebou Adams on loan until January.
Adams, 21, signed from non-league Dartford in February 2016, will be making his second loan move from Carrow Road, having had a brief three-game stint with Braintree last season.
Jules, 20, did not play a first-team game for the Royals.
But he did make 10 Scottish Premiership appearances for Motherwell during a loan spell last season, and he was a member of the Scotland Under-20 squad that finished third at the recent Toulon tournament.
Shrewsbury have now made five summer signings, having previously brought in strikers Lenell John-Lewis and Arthur Gnahoua and midfielder Jon Nolan.
Find all the latest football transfers on our dedicated page.
Shrewsbury Town have signed teenage Reading defender Zak Jules for an undisclosed fee on a two-year contract.