Lathrope, 28, is a defensive midfielder who started his career in Norwich City’s academy in 2006, signing a professional contract with the Canaries in 2008.
He joined Torquay in July 2010, playing over 100 matches in League Two, helping them reach the League Two play-offs in his first two seasons there, before leaving in 2014 to join Aldershot Town.
He spent two seasons with the Shots, re-joining Torquay at the beginning of last season.
Lathrope joins the Cards on a contract until the end of the 2018/19 season.
Woking manager Anthony Limbrick said: “Damon is a very good signing for us, as he is experienced at this level and knows the league. He has a great attitude, will be able to add value to the younger players, and use his professionalism to be a leader both on and off the pitch.”
Lathrope commented: “I’m over the moon to be at this great club and can’t wait to get working with the team and manager. I’m a defensive midfield player, I like to pass the ball, quite comfortable off both feet, I’ll win the ball back and give it to the players who are going to go score the goals!”