The 19-year-old striker has signed a two-and-a-half year contract with Yeovil after impressing during a loan spell.
A product of Liverpool's academy, Morgan made three first-team appearances for the Anfield club, all in last season's UEFA Europa League.
Several other players sealed temporary moves away from English top-flight clubs on Friday.
Swansea City defender Alan Tate has joined Scottish Premiership side Aberdeen on loan for the remainder of the season.
Tate, who captained Swansea in their first Premier League fixture in August 2011, previously spent time at Yeovil this season before a hamstring injury cut short his stint at Huish Park.
Arsenal have confirmed goalkeeper Damian Martinez will remain on loan with Sheffield Wednesday for the rest of the campaign.
Martinez initially joined the struggling second-tier club in October and has played in six matches to date.
Stoke City midfielder Jamie Ness, meanwhile, has joined League One promotion-chasers Leyton Orient on a 28-day loan.
A peripheral figure at the Britannia Stadium, Ness has yet to represent Stoke in the Premier League since arriving from Rangers in July 2012.
