He was arrested Wednesday and sent to Liberia where he was met by U.N. officials and immediately flown to Sierra Leone.
Taylor and members of his family were captured Tuesday night in northeastern Nigeria as they tried to cross the border into Cameroon by car.
Also in the car were two 110-pound sacks filled with U.S. and European currency, according to Nigerian police officials, reported the Associated Press.
Obasanjo said he felt "vindicated" by the arrest of Taylor, which came just before a meeting with President Bush. The issue had threatened to create tension during the meeting since the United States had called on Nigeria to turn over Taylor to the war crimes tribunal.
Obasanjo said the mood of the White House encounter "changed drastically" with the announcement of Taylor's arrest.
News that Taylor had disappeared from his secure compound in Nigeria where he had lived for nearly three years came just an hour before Obasanjo left Nigeria for Washington.
White House officials had suggested the meeting might be canceled if Nigeria's leader was unable to provide answers for President Bush about Taylor's disappearance. Some analysts had suggested the Nigerian government might have been complicit in his disappearance.
During a news conference, Obasanjo said those who spread such ideas "are wrong and owe an apology."
Taylor has been living in exile in a palatial compound in Nigeria since 2003 when he stepped down as president of Liberia as part of a deal to end the country's 14-year civil war.
Until recently, Nigeria had resisted sending Taylor to Sierra Leone where he is to face allegations of war crimes related to Sierra Leone's 1991-2001 civil war.
Taylor is charged with supporting and helping organize Sierra Leone rebels, including brigades of child fighters, who terrorized victims by chopping off their arms, legs, ears and lips. He would be the first African leader to face trial for crimes against humanity.
Obasanjo agreed to surrender Taylor to the war crimes tribunal at the request of Liberian President Ellen Johnson-Sirleaf. The United Nations and United States also have pressured Nigeria to extradite Taylor.
"It's a great relief that he's been recaptured," U.N. Secretary-General Kofi Annan told reporters in New York. "I think his capture and being put on trial does not only close a chapter, but it also sends a powerful message to the region that impunity will not be allowed to stand and would-be warlords will pay a price."