Upon the establishment of any such county court the Governor, upon the recommendation of the members of the General Assembly from the county in which such county court has been established, shall appoint for such county a resident attorney at law as county solicitor, whose term of office shall continue until his successor shall have been elected by the qualified electors of the county at the next succeeding general election and until his successor qualifies. After the first term herein provided for, the term of the county solicitor shall be for four years and until the election and qualification of a successor, the qualified electors electing such successor at the general election occurring every four years.