The 18-year-old has completed a medical and will link up his new team-mates following the international break.
City boss Lee Johnson told the club website: “We are always on the look out for quality and Jonathan has that.
“He also brings genuine pace and versatility in the forward areas.
“Thanks to Tony Pulis and West Brom for allowing the deal to happen.
“It’s now up to Jonathan to work hard for the team and express his talent in a City shirt.”