The iconic midfielder, who made his name in the 1990 World Cup finals in Italy, has agreed in principle to join the Pilgrims.
He will join the club as player-coach, and will make his debut tomorrow night in a pre-season friendly against his first club Newcastle United.
Gascoigne said: "I've spoken to Boston and I was really pleased with what they had to say and the chairman's ideas about what he wants to do with the club,.
"The manager, Steve Evans, also seems a great guy, so I'm quite happy with what they have to offer."