David Thomas, a former chief executive of Melrose Resources, had stepped down from the board of Petroceltic. He will retain an executive role as chief operating officer. This will include regular attendance at board meetings.
Tom Hickey, chief financial officer of Petroceltic, has stepped down from the board on the same basis.
Hugh McCutcheon and Dr Robert Arnott have resigned as non-executive directors
The changes follow last month's decision by Worldview Capital Management to drop its opposition to a $100 million (£60 million) share placing by Petroceltic in return for concessions.
Petroceltic agreed to shrink its board from nine to seven members. Worldview, which has a 20 per cent stake in Petroceltic, won the right to recommend two independent non-executive directors.
Don Wolcott and Joe Mach have been appointed non-executive directors of Petroceltic on Worldview's recommendation. Both men held senior positions with the Russian oil and gas firms Ruspetro and Yukos.
Petroceltic's chairman Robert Adair and chief executive Brian O'Cathain will retain their board seats. Mr Adair founded Melrose.
Petroceltic acquired Melrose in a £165 million deal in 2012.