The 27-year-old was officially a free agent following his release by Chesterfield at the end of last season.
Gulls boss Martin Ling made a move for the player after watching him appear as trialist for Yeovil in their win over Plymouth last weekend.
Despite being the victim of two serious knee injuries, Ling is confident that Downes can flourish at Plainmoor.
"He was going to be a massive product at Chesterfield but has suffered a couple of bad knee injuries," he told the club's official website.
"These have definitely thwarted his career in terms of where he wanted to go and he is looking to rebuild. He wants to go back to where he was aiming."