In his appeal to the Spanish government on Monday, the 28-year-old had said that his life was in danger because he refused to support his father.
His request for asylum came immediately after he arrived at Madrid's Barajas airport on an Egypt Air flight from Cairo.
Omar lives in the Egyptian capital with his 52-year-old wife, formerly known as Jane Felix-Browne.
The decision to reject the asylum petition met the rules of the United Nations High Commissioner for Refugees, a spokesman for Spain's interior ministry said.
"He was notified of the decision early this afternoon," he said.
In April, Britain prevented Omar from settling in the country, saying that his asylum would arouse "public concern".
He had said that he wanted to live in England with Zaina at her home near Northwich in the northwestern county of Cheshire.
Renunciation of violence
While he has condemned violent acts in media interviews, Omar has declined to directly condemn his father, particularly over the September 11, 2001, attacks.
"Those who know the Arab culture understand that sons are not allowed to publicly attack their fathers. This is cultural," the statement released on Wednesday by Omar and his wife said.
"This does not mean that Omar agrees with his father's activities. He does not … Only those who truly know the Arab culture will realise Omar's bravery in taking a stance for peace against his father."
Omar is the fourth of 11 children born to his father's first wife, and he is one of 19 children Osama bin Laden has fathered.
The couple said that their decision to leave Egypt for England "had nothing to do with any actions of the Egyptian government".
"There were outsiders working within Egypt which created genuine concern for Omar's safety. That is the only reason we left Egypt," the statement said.