Alessandra, 24, snubbed the offer of a new deal at Morecambe to agree a two-year deal at Home Park.
He previously played under Argyle manager John Sheridan at Oldham, and the Pilgrims boss said: "I'm very pleased to have signed him; I think he's at a good age and he can be a really good player for us.
"When he first came on the scene I thought that potentially he could play at a really high level but he took a bit of a backward step when he was at Oldham.
"Fair play to him, though, he went to Morecambe and sorted himself out and for the last two seasons he's probably been Morecambe's most consistent player.
"He's got a lot of things to his game - he can play on the wing and anywhere across the so-called front four - but I like to see him up front.
"He reminds me of Jack Lester, who was at Chesterfield. I think he's got the attributes to be that kind of player and I think I can get the best out of him and get him to score goals."