The 29-year-old left-back has rejoined the club for a third spell from Blue Square Premier outfit Barrow, where he made 26 appearances last season.
Jelleyman has played for the Pilgrims twice on loan, first during the 1998/99 season and then during the 2004/05 campaign.
The acquisition of the former Wales Under-21 international means United's managerial duo of Paul Hurst and Rob Scott are just one signing away from completing their summer shopping list.
"It is quite a coup to land a player of Gareth's quality," declared Scott. "We have bided our time and are delighted to welcome Gareth onboard."
A goalkeeper to provide competition for Aaron Butcher is Scott and Hurst's next target ahead of United's Blue Square Bet North opener against Stafford Rangers on August 14.