North Yorkshire Police said the man and woman had climbed 60ft up a rig at Third Energy's site in Kirby Misperton, near Malton, in the early hours of yesterday (Saturday).
The force said that the 21-year-old woman and the 28-year-old man were arrested on suspicion of aggravated trespass and criminal damage when they climbed down today.
The pair, who were among three protesters to originally scale the rig, remain in police custody.
Superintendent Mike Walker said: “This incident has thankfully been brought to a safe conclusion.
“From the outset, the safety and welfare of the individuals who had climbed the rig was of paramount importance.
“We work with all those involved to make sure any protest activity is as safe and peaceful as possible, however, we have a duty to take appropriate action if this activity poses any danger."
All the protesters had been issued with safety harnesses yesterday and were being helped down safely from the rig by police officers.
The woman came down at 10am and the man at 10.25am.
Police had previously helped a 29-year-old man to climb down from the rig at around 3.45pm yesterday.
He was arrested on the same charges at the other two protesters and remains in police custody.