Farbrace has quit his post as second team coach to become head coach of Sri Lanka.
Yorkshire say they are in no rush to replace the 46-year-old, who takes up his new job on January 1 having signed a two-year contract.
Possible candidates to replace him include former Yorkshire and England all-rounder Anthony McGrath, who has been doing some coaching work at the club.
Farbrace had retained strong links with Sri Lanka having been their assistant coach from 2007 to 2009 and he had been favourite to replace Graham Ford, the outgoing coach, who is joining Surrey.
Farbrace admitted it was a wrench to leave Yorkshire, where he has helped oversee the club’s young talent.
“It has been a difficult decision, probably the hardest of my career,” he said. “It is a great opportunity, but it is tinged with a bit of sadness to be leaving such a fantastic organisation.
“I have thoroughly enjoyed my two years here. I have learnt a massive amount in the time I’ve been here and it has enhanced my development as a cricket coach.”
Farbrace, who will join Sri Lanka on their ongoing tour against Pakistan in the UAE, initially rejected interest from his former employers when it became clear Ford was on his way.
However, a lack of quality candidates reignited Sri Lanka’s pursuit.
“International cricket is something I was keen to do again at some stage further down the line and when this opportunity came up, I had to make a tough decision,” said Farbrace. “It is the highest form of the game and to test myself in that arena will be a great challenge.
“I spend a lot of time encouraging players to be the best they can be and continually to challenge themselves and this is what I have to do.
“Sri Lanka is a fantastic place – packed full of great cricketers – and the next generation of international players are steadily coming through.”
Farbrace will be back at Headingley in June when Sri Lanka play the second of two Test matches against England.
He leaves believing that Yorkshire are in excellent shape.
“The club is well set to deliver long-term success both on and off the field,” he added.
“There is a desire, from top to bottom, for the club to be a leading light in the game.
“Everyone is working hard behind the scenes to reach the potential this great county deserves.”
Yorkshire chief executive Mark Arthur praised Farbrace’s work and said the county would take their time over his replacement.
“We will sit down over the next few weeks and work out what is the best strategy for Yorkshire cricket,” he said.
“We are in no rush to fill the role and want to consider all our options.
“We have some quality people within the cricket department and their opinions will form the basis of our plans for the long-term benefit of professional cricket.”