Morgan has signed a two-and-a-half-year contract with the club after making the switch on loan to the Glovers in November.
The 19-year-old broke into the Liverpool senior side under Brendan Rodgers at the start of the 2012-13 season and made a total of three first-team appearances.
Morgan took to his official Twitter account to thank LFC fans for all their support, and said that he is hoping this permanent move will be a huge stage in his career.
"Thank you for all the messages off LFC fans, [it] means a lot to me," Morgan said.
"I spent so much of my life at Liverpool and loved every minute - the ups and the downs.
"Liverpool is always the team I will love and support, and always where my home will be, but it's time for me to show what I can do at my new club.
"I am really looking forward to what I hope to be a huge stage of my career."