Bath owner Bruce Craig is to step down as chairman at the end of the year.
Griffiths led a review into Bath’s poor start to this season – they have lost all their matches – and recommended hiring a dedicated defence coach.
“I will continue to support the club emotionally and financially and do whatever I can for the club to be successful,” Craig told Bath’s website.
“Ed has played a leadership role with Rugby World Cup and Premiership-winning teams and brings a wealth of knowledge and experience to Bath Rugby.”
Bath have been beaten in all nine of their Premiership fixtures and are 10 points adrift at the foot of the table, although with no relegation this season the club will not drop out of the top flight.
They were also brushed aside in their opening Champions Cup match earlier this month as Leinster scored seven tries to run out 45-20 winners in Dublin.
Bath have announced that Munster boss Johann van Graan will join the club as head coach next season, while fellow South African Brent Janse van Rensburg has been brought in as defence coach for the remainder of this season.
Multi-millionaire Craig made his fortune in pharmaceuticals and moved the club’s training facilities to Farleigh House.
But plans for a new stadium to replace The Rec have yet to bear fruit, despite Craig aiming for a new 20-25,000 capacity venue when he took the club over.
“We will continue to invest in the resources and capabilities required to achieve success,” added Bath chief executive Tarquin McDonald.