Green, 23, came through the ranks at Everton and moved to Boston from Chester in the summer.
He said: "Unfortunately things haven’t gone as planned at Boston, mainly due to the brilliant run of form they have been on so it’s been difficult trying to nail down a spot there. I was open to a short move away to get a decent run of games and those all important minutes in my legs.
"I know Gainsborough is a good club, and has a good fan base and I just can’t wait to get out there and get going. I'll give my 100% throughout my time here, I’m a winner and love winning football matches. I’m hoping I can help the club climb up the table to a position which they deserve quite rightly to be.
Green missed out on the chance to make his debut at the weekend as the Holy Blues league game with Stalybridge Celtic fell foul of the weather.
Manager Curtis Woodhouse said: “I am delighted to get George Green in from Boston United.
"He is a really, really talented central midfielder that will give us that bit of extra quality in the final third. George has a great left foot and great technical ability that I’m hoping will really make him a joy to watch."