Lathrope was out of contract at Plainmoor this summer but, having been an influential player in the club's failed promotion charge this term, he will now look to help the Devon outfit go one better next season.
The 22-year-old, who arrived from Norwich in 2010, is due to put pen to paper later this week.
Gulls boss Martin Ling told the club's official website: "Damon is a scenario where an offer was put on the table and he has been an integral part of what we've done this season.
"I want him to stay and it has always been a logistics thing with Damon, but he has agreed to the new deal which is great news for the club.
"It is always a great barometer of a player's influence by how he is judged in the dressing room and Damon's performances have won him the respect of his team-mates. He allows us to play a certain style of football with his disciplined approach and this new deal is reward for his terrific contribution to the team."