The 21-year-old has recently returned to Ashton Gate after a loan spell at Bristol Rovers, where he made 18 appearances without scoring.
"There was a lot of interest in John and he has opted for a move to Dagenham," said City boss Keith Millen.
"Hopefully he will go there and get some first-team games under his belt. He needs to give his career a real kick-start."
Source: PA
Source: PA