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.

America Luke Richardson sent about 4,000 messages to a 14-year-old girl from Essex and met her in a hotel, Greater Manchester Police (GMP) said.
The 22-year-old had previously been dismissed by the force after he stole uniform and visited schools without authorisation.
Richardson, of Salford, was sentenced at Manchester Crown Court.
He was also given a sexual harm prevention order and will be on the sex offenders' register for life.
He admitted six counts of sexual activity with a child, one of grooming and one of taking indecent photographs of a child.
GMP suspended Richardson in January 2014 after finding he had "used his role inappropriately" while entering a school without authorisation on an independent patrol.
But, after removing his uniform and warrant card from him, Richardson was again found to have gone to a sixth form college while wearing police uniform.
On searching his home, officers found a large quantity of police uniform to the value of Â£970 and arrested him on suspicion of theft.
Subsequent allegations of inappropriate contact with children prompted a new investigation in September 2015.
Richardson's confiscated phone and computer revealed 4,000 messages had been sent to a 14-year-old girl in Essex.
She revealed they had met up in a hotel booked by Richardson.
He was then charged with a number of sexual offences and remanded in custody before being formally dismissed in April.
Supt Mark Kenny said: "I am pleased that America Luke Richardson is now off the streets and unable to harm any more young girls.
"We are continuing to investigate the possibility that Richardson may have more victims and we are appealing for anyone who may have been approached inappropriately by him online, or in person, to come and speak to police."
Shrewsbury Town have signed teenage Reading defender Zak Jules for an undisclosed fee on a two-year contract.
[NEXT_CONCEPT]
A former special constable who groomed and engaged in sexual activity with a child has been jailed for five years.