Ganiyatu Sanusi, who has been in custody for nearly seven months, was immediately released after the three judges ruled that Mr Straw had made "an invalid deportation order".
Lords Justices Evans, Ward and Brooke ordered their judgment to go directly to Mr Straw and that he should take notice of their comments when he reconsiders Ms Sanusi's application to stay in Britain.
'Precedent for hundreds'
Cal Harding, a US lawyer who represented Miss Sanusi without a fee after her legal aid was withdrawn two days before the appeal court hearing, said the ruling will affect "hundreds of others" who are seeking asylum in Britain.
Miss Sanusi, who married a British citizen nearly two years ago, was in tears after her release. "I am so happy now. This means I can now go back to college to study accountancy," she said.
Mr Harding said the appeal court had ruled that the home secretary had no powers to serve deportation and refusal of asylum orders simultaneously.
"When she was served with deportation orders this requires her to leave the UK immediately. The secretary of state has no powers to require her to leave when she still has the right to appeal," he said.
Lord Justice Brooke pointed out that although the original deportation order was quashed, the home secretary could make another order immediately.
"We can assume, however, that he would not do so without first giving anxious and careful consideration of the circumstances of Miss Sanusi as they now are."
He added: "She has now been in detention for six months as a consequence of the making of an invalid deportation order. These are matters which the secretary of state will take into account when he reconsiders his decision in this case."
The judges also refused the Home Office leave to take the case to the House of Lords.
Three-year fight to stay
Miss Sanusi, who has been in Britain since she was 13, had lost an appeal against deportation in 1995. She had sought asylum based on her father's political involvement with the late opposition leader Chief Abiola.
She withdrew her claim in 1996 when the adjudicator asked the home office to look into her case. But the Home Office upheld their decision to deport her and she renewed her application for asylum which was again refused.
After she married in January 1997, she re-applied for asylum and was turned down despite representations from her MP.
Miss Sanusi, who lives in London, was arrested in May and held in custody as an overstayer.
Nigerian fighting deportation
The ruling comes two days after another Nigerian lost his appeal against deportation.
Commodities broker Ben James, from Dulwich in south London, failed to block his removal to Nigeria and is planning a last-ditch plea to Home Secretary to show him compassion.
Mr James, who has received backing from Health Minister Tessa Jowell, says he faces the loss of his business, his home and the jobs he has created for others.
He said he was extremely afraid: "They could now arrest me and put me on a plane to Nigeria, a place where I don't know anybody, have no friends or family and don't speak the language."
Northern Ireland
Scotland
Wales
England
Nigerian in final bid to beat deportation
(14 Dec 98 | UK)
Immigrants 'should not be held in jail'
(11 Dec 98 | UK)
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