IRFU high performance director David Nucifora said the Irish governing body had received a “huge response” to the job advertisement.
“Adam has developed into an outstanding coach since arriving in Ireland in 2009 and has coached at schools, club and inter-provincial level,” said Nucifora.
“He has good knowledge of the women’s game in Ireland having brought success to the Leinster women over the past season.”
Griggs said that he was “delighted” at his appointment, adding that there is a “huge pool of talent” in Ireland.
“It’s a new challenge for me, but it’s an exciting one. This is a fresh start for all of us within the squad and I know the players are highly motivated to do well,” said Griggs.
Tierney left the Irish role after the hosts’ disappointing performance at this year’s World Cup.
Former international Ruth O’Reilly and current player Jenny Murphy were among those who strongly criticised the IRFU’s announcement that the next coach would be a part-time appointment.