The 26-year-old, who moved to Home Park from Morecambe in 2013, has been Argyle’s second top scorer for the past two seasons.
Alessandra’s contract at Plymouth had come to an end and he expressed a desire to move back to Lancashire, where his family live. He had scored 25 goals in 100 games for the Pilgrims.
In a statement posted on his Twitter feed, Alessandra said: “I want to thank everyone at PAFC, sad to be leaving a really great club.
“I loved every minute in a green and white shirt and like to think I gave I my all.
“I hope people understand my decision of wanting to be closer to my son and family.
“Want to wish everyone at the club, the lads, staff and the fans all the very best in the future.”