Clark, a former player with Clevedon United, scored twenty-five goals for Chard in the First Division of the Toolstation Western League during the past season.
He was signed last summer by Chard boss Glyn Shaw who has since left the South Somerset club.
Bridgwater earlier strengthened their squad with two other new signings - Bideford's 27-year-old striker Dave Pearce and 25-year-old former Team Bath and Clevedon Town midfielder Matt Thorne.
"We are still able to attract quality players, despite having had an indifferent season," said boss Rob Dray. "They will give us experience down the middle of the park."
Bridgwater's only disappointment of the close season has been the loss of experienced striker Chris Young, who has joined Blue Square Bet South neighbours Weston-super-Mare.