Wilson Hartnell has begun the recruitment process to replace Finlay, who has been director of public affairs for three-and-a-half years.
Rabbitte replaced Rauri Quinn as Labour leader two weeks ago, becoming the first leader of the party to be elected directly by party members.
The next national elections are four-and-a-half years away, a period in which Finlay will advise Rabbitte on party strategy, covering policy, comms and public affairs.
He is working out his notice with Wilson Hartnell and expects to start full-time work for Rabbitte 'within the next couple of weeks'.
Finlay, who writes for the Irish Examiner, held a variety of governmental press and adviser posts in the 1980s and 1990s.