The 30-year-old, who gained his first taste of the Football League with Aldershot, was released by League One Shrewsbury earlier this summer having bagged 18 goals in two years at the Shropshire club, including seven last season.
Morgan rejected other interested suitors, including some from League One, to pen a deal at Home Park and he is delighted to have joined the Pilgrims.
He told the club's official website: "As a striker, you want to be playing, you want to be scoring goals, and you want to be going to an ambitious club, and you can't be getting a more ambitious club than this in League Two.
"This is the biggest club I have played for in my career.
"It is about trying to get it out of League Two and into League One and going on from there. It's going to be a tough task, but my ambition is to do what I did at Shrewsbury, when I took a step back to move forwards.
"It was the right step to go to Shrewsbury when I did, and I think it's the right thing again.
"I did have offers from League One clubs, even a last-ditch effort from a team last night (Sunday), but I'm a man of my word and, once I got down here, my mind was made up.
"At the moment it's hard for any player getting a team and I was grateful to have a few teams interested in me."