Abdullah, 86, flew to New York for medical treatment Tuesday after suffering from a slipped disc and being diagnosed with a blood clot pressing on the nerves in his back.
The king had "a back surgery, in which the blood clot was extracted, the slipped disc was corrected, and the injured vertebrae was stabilized in Presbyterian Hospital in the United States of America,'' the Saudi Press Agency quoted the statement as saying.
"The operation was accomplished successfully,'' it added. The king temporarily handed control of the world's top oil producer and key American ally to his half brother and heir to the throne as he left.
Before the king headed for New York, Saudi officials had been making a strong push to reassure the public and international allies there is nothing to worry about and late on Tuesday Crown Prince Sultan said that the results of tests were as good as could be expected.
Abdullah has temporarily handed over authority in the past when he has traveled abroad for conferences or personal trips, though this was the first time for health reasons.
Monday's smooth transfer of power from one brother to another served as a reminder of the advancing age of the generation of the royal Al Saud family that has ruled the kingdom for the past 60 years.
It also revived a long-standing question that may be taking on greater urgency: Can the rulers maintain stability when it comes time to pass the throne to a new generation.
The 85-year-old Sultan -- also the defense and aviation minister-- has his own health issues: He underwent surgery at the same hospital in New York in February 2009 for an undisclosed illness and spent nearly a year abroad recuperating in the United States and at a palace in Agadir, Morocco.
Abdullah rose to the throne in 2005 after the death of King Fahd, though he had already been a de-facto ruler for half a decade.