Dewani was driven away from a south London jail under a blanket in the back of a luxury sport utility vehicle, after a High Court judge rejected South African appeals to keep him in custody during the extradition process.
South Africa wants 30-year-old Dewani on suspicion of paying to have his bride Anni killed in Cape Town.
The 28-year-old was shot dead on November 13 after the couple's taxi was said to have been hijacked.
Taxi driver Zola Tongo said in court on Tuesday that he had been offered R15 000 Dewani to kill his wife.
Dewani strongly denies any involvement.
Tongo has already received a reduced sentence for murder as part of a plea bargain.
The South African authorities were concerned that Dewani would not appear at an extradition hearing in Britain later this month if he was allowed bail.
Extrdition warrant
However, Duncan Ouseley, a judge at the High Court in London, disagreed on Friday and allowed his application.
Dewani, a care home owner, handed himself in to a police station in Bristol, southwest England, on Tuesday.
He appeared at the City of Westminster Magistrates' Court in London on an extradition warrant on Wednesday.
He was granted bail but the South African authorities appealed, meaning he stayed in custody.
Dewani was being held at Wandsworth Prison - the same jail where WikiLeaks website founder Julian Assange is awaiting the outcome of moves to extradite him to Sweden.
Dewani's release from custody comes under stringent bail conditions.
Black market
Lawyer Ben Watson, representing South Africa in the court on Friday, said "significant new evidence" had emerged showing there was "a very powerful case against Mr Dewani" which increased the risk of him taking flight if allowed bail.
He told the judge this included new security camera footage and evidence that Dewani had obtained money on the black market, allegedly to fund the murder.
Dewani's lawyer Clare Montgomery said he was being accused by a group of self-confessed robbers and murderers with "everything to gain and nothing to lose" by implicating Dewani.
Dewani's spokesperson, the publicity guru Max Clifford, said his relatives were "very pleased" with the decision.
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