The 21-year-old was allowed to leave Yeovil following their relegation from League One and Stanley have swooped to bolster their attacking options.
Morgan, who has also been on loan with Rotherham and St Johnstone, played three games for Liverpool in the Europa League in 2012.
“The manager’s given me this opportunity and the chance to play football and that’s all I’ve ever needed,” Morgan said.
“I just want to show people what I can do and this club has given me the chance. I don’t want to let myself or the club down.
“I’m a goalscorer and I need to be on the pitch as much as possible. I feel like I will score goals if I get time on the pitch so I want to play as many games in a row as possible, get in my stride and all I need is one goal to get going.
“Liverpool is all back in the day for me. It was a great time to be at the club but I can’t dwell on Liverpool. I don’t really want to talk about what happened at Yeovil but it wasn’t a nice time for me and I just want to start again here.
“I know that you don’t become a bad player overnight and I want to prove that I can still score goals and contribute to the team.”
Accrington boss John Coleman hopes Morgan grasps his chance in east Lancashire.
He added: “We haven’t got that many forwards and it’s a chance for Adam to resurrect his career.
“He has a great pedigree, he is highly thought of at Liverpool and he will be as frustrated as anyone that it hasn’t got going for him.
“This is an opportunity for both of us and hopefully Adam will grab it with both hands.”