Nigel Adkins' Royals, recently relegated from the top flight, will make the trip on Wednesday July 24 before City round off their pre-season preparations at Bournemouth three days later.
"It's a good way to end pre-season," head coach Sean O'Driscoll said. "We play a team that have come down from the Premier League in Reading and arguably the best team in League One last season, Bournemouth, in the days leading up to the first league fixture.
"Nigel rang me up and asked for the friendly at Ashton Gate and we were pleased with the opportunity. I think he'll be looking to tinker with the dynamics of Reading's play slightly this season and it'll be a meaningful game for them, as it will us."