"In the light of the uncertainties surrounding the status of my work visa and the sustained harassment of the company and myself, I have decided to leave and to work outside Russia temporarily," Dudley said in a statement obtained by The Times of London.
Officials granted Dudley a temporary transit visa. He was denied a work visa because Moscow says he lacks a proper employment contract.
"I have taken this decision after appropriate reflection, on the basis of unequivocal external legal advice, and I shall continue as chief executive of TNK-BP, group chief executive and chairman of the management board," he said.
Russian shareholders in the consortium say BP is thwarting the company's attempts to expand and have moved against Dudley in recent months. Analysts see the move as an attempt by the Kremlin to insert Russian energy giant Gazprom into the merger, an allegation Moscow denies.
Dudley said in his statement he would continue his duties as his position mandates.
"During this period I will continue to discharge my duties, and I have all necessary authority to do so. I have been advised that this temporary exercise of authority whilst outside Russia is both lawful and better for all shareholders than the alternatives," he said.