The deal ends months of speculation about the future of the Gulls, who were facing financial difficulties.
"There is relief that the club is saved. We were looking at a serous financial situation," outgoing chairman David Phillips told BBC Sport.
The deal is subject to ratification by the National League and supporters have raised concerns about GI.
The group pulled out of a bid to buy the club in the summer.
However, Phillips said Torquay had been close to going into administration and added: "This deal had to be done.
"All of the other people that were supposedly in the background, I've spoken to Chinese, Hong Kong and American, we asked them to to put some money in to save the club and it was never forthcoming."
Nobody from the new owners was at Plainmoor to talk about the deal.
"I would like to take this opportunity of assuring everyone connected with, and supporting, the club that we will try our best to secure the club's long term future," said GI head Clarke Osbourne in a statement.
"Our initial work is to ensure that the club is stable whilst compiling a five-year plan to secure the club's future and bring high-level football entertainment to Torbay."
There has been talk of the club leaving their Plainmoor home for a new ground on the outskirts of the town, a plan which the Torquay United Supporters' Trust has questioned.
"With GI, our biggest concern is that they are a property developer, they have very little interest in football apparently and they have very little connection with Torquay as a place," TUST spokesman Alan Robinson  told BBC Sport.
"I totally understand the financial constraints the club is under. We understand that at this moment in time GI was the only option.
"Our concern is over the last 18 months we have at least twice or three times developed the opportunity of commitment ownership."
National League club Torquay United have been taken over by Swindon-based Gaming International (GI).