Watt left his previous role as manager of Margate last Monday.
He makes his return to the Gallagher after two and a half years.
He originally joined the Stones from Dover Athletic in March 2013, following a month on loan, and made 89 appearances.
"I wanted someone who knew the club, knew how I worked what I was about," Saunders told the club's website.
"I spoke to him a time ago about him potentially coming in as a player-coach."
Saunders says there was a lot of interest in the role.
"There were a lot of people who applied and wanted to meet me to talk about it.
"I knew how important it was to get this position filled with the right person and that is what has happened."