Todea, formerly prefect of Salaj county and government inspector, had chaired the board since November 2011.
Ciutureanu is a Constanta county councilor on behalf of the Liberal Party (PNL).
Oil Terminal announced Todea had expressed in writing his intention to resign.
The company is 59.62% owned by the Economy Ministry, while investment fund Fondul Proprietatea holds 8.45%.
On Monday, Oil Terminal’s shares traded up 3.05% at RON0.135 in Bucharest. (EUR1=RON4.4594)