Alessandra became a free agent this summer after departing League Two side Carlisle United and makes his first move into non-league football having spent 15-years in the Football League.
Alessandra spent the 2016-17 campaign at the Suit Direct Stadium where he scored nine times in 50 appearances across all competitions.
The 33-year-old has enjoyed spells at Plymouth Argyle, Rochdale, York City, Morecambe and Notts County before his two year stint at Brunton Park.
Alessandra is the latest player with a Pools connection to make the move to the 1st Cloud Arena to join former Sunderland striker Kevin Phillips after midfielders Martin Smith and Michael Woods and defender Gary Liddle.
Smith left the Suit Direct Stadium at the end of last season after just one year with Pools, whereas club legend Gary Liddle rejected a new deal with the club before joining the Mariners for their anticipated promotion push, with Woods joining from York.
“South Shields is definitely a club on the up and going places with big aspirations, so I’m delighted to be part of it,” Alessandra told the club website.
“They made me feel very wanted, which was a big factor in my decision, and I can’t wait to get started.
“I knew a few of the lads here already and they said everything I wanted to hear in terms of the set-up and the way the club goes about things.
“I had a chat with the manager, who has great pedigree as a forward himself, and it will be great to get the chance to learn from him, even at my age.”
South Shields manager Kevin Phillips said: “Lewis is another fantastic signing for the club.
“He is someone who has only ever played league football, so to attract a player of his calibre is a massive coup.
“We’re naturally delighted to have him as he brings added competition to the squad and excellent quality, alongside the players we already have in that position.
“He brings brilliant pedigree, experience and leadership qualities, and fits well with the players we have signed this summer and those who were already here.”
The Mariners begin their Northern Premier League campaign at home to Stalybridge Celtic on Saturday, August 13.