The boards of supervisors of two or more counties may enter into an agreement to jointly employ a county engineer, employ professional and clerical assistants for the engineer, and to provide such services as can be carried on jointly and will operate to their mutual benefit. Such agreement shall be written and entered in their respective minutes. The engineer employed under such agreement shall be the official county engineer for each of the respective boards and shall be employed for such term of years as shall be determined by the boards but in no event longer than the period of time the mutual agreement between the boards is to be in effect. The written agreement shall provide for the determination of the cost of such joint program and the manner of allocation of the cost to each board for inclusion in the respective budgets. The boards by mutual agreement shall designate one board to make payments for salaries and other costs of the joint program. The board shall be reimbursed by the other board or boards in accordance with the joint agreement. The provisions of chapter 28E shall be applicable to this section.