Edinburgh-based Bowleven said Mr Brown intends to resign as finance director to take up a similar position with an energy services firm in the United Arab Emirates, which it did not name.
A spokesman for the company said Mr Brown will be paid up to his expected resignation date early in the new year but receive no compensation for loss of office.
Mr Brown, 49, has spent nine years at Bowleven during which the company has mainly focused on its acreage off Cameroon.
In his time at the company Bowleven has completed a series of fundraisings.
Last month the company raised £13 million from investors at 45p per share but said a decision about whether to sanction the investment required to bring fields off Cameroon into production had been delayed until next year.
Bowleven raised funds at 650p per share in October 2005, 10 months after it floated on the Aim market.
Mr Brown was recruited to the team led by former executive chairman Terry Heneaghan. Kevin Hart became chief executive at Bowleven in November 2006 after the company had suffered drilling disappointments.
Ronnie Hannah became chairman a month later.
Chief Tabetando, a lawyer from Cameroon, has been on Bowleven's board since 2001.
Peter Wilson, who has advised the company on legal matters since 1999, became a director in 2005.
Mr Hannah said: "John has been an integral member of the Bowleven team and I wish him all the success in his future new role."
Mr Brown will be replaced by his deputy Kerry Crawford.