WASHINGTON—Chevron is regaining the ability to pump oil in Venezuela from the Trump administration, people familiar with the move said, in an abrupt reversal in the White House’s policy toward the socialist dictatorship.

Details of the agreement were still unclear, but it follows recent discussions involving President Trump and Secretary of State Marco Rubio and comes amid last week’s prisoner swap that released all 10 remaining Americans who were detained by the Venezuelan government, people familiar with the matter said.