Morgan, 19, an England Under-20 international, who has made three appearances for the Reds, will sign permanently when the January window opens.
"Adam has been generating a lot of interest recently, he had a lot of options but he has chosen to come to us," manager Gary Johnson told the club's official website.
"We are taking him on a deal until January and then he will join us on a permanent contract after that.
"Adam is a great prospect, I personally feel he is ready to play Championship football now.
"I remember Robbie Fowler saying that Adam is one of the best finishers he has seen in a long time. That is big praise."
Morgan's addition comes at the end of a busy day for the Glovers with Miller and Lundstram also joining on loan.