The ad for the new Garda Commissioner will say policing experience is 'desirable, but not essential'.
Justice Minister Charlie Flanagan has formally asked the Policing Authority to start the process to hire Noirín O'Sullivan's replacement.
The application process will be an open competition, and the authority will consider international candidates.
The salary, approved by Cabinet, is reported to be in the region of €250,000.
In a statement, Minister Flanagan said this is the first time there will be an international competition for the job overseen by the independent Policing Authority.
He explained: "It marks a very significant change in the manner in which this important office will be filled.
“The overriding concern must be to ensure that the best candidate is selected to lead An Garda Síochána. This requires that the process attract the widest possible field from a broad range of backgrounds."
He added: "It is for this reason that the Government has agreed that there should be no bar imposed in terms of nationality, or indeed, previous experience of policing."
Minister Flanagan has indicated it "could take up to a period of six months" before the next Garda chief is identified and appointed.
Mrs O'Sullivan's retirement came on the back of calls for her to resign over the controversy involving false Garda breath test data.
Announcing her decision to leave the role, Mrs O'Sullivan expressed frustration "that the core of my job is now about responding to an unending cycle of requests, questions, instructions and public hearings".
Donall O'Cualain is serving as Acting Garda Commissioner, and has previously ruled himself out of applying for the permanent post.
Reporting by Sean Defoe and Stephen McNeice