Assange has already spent a week in a UK jail following his surrender to British police over a Swedish sex-crimes warrant.
He denies any wrongdoing and has already refused to voluntarily surrender to Sweden's request to extradite him for questioning.
In a day of courtroom drama, the 39-year-old Australian was first told by a judge that he would be freed, then less than two hours later was informed he had at least another 48 hours in custody.
Britain's High Court will hear the Swedish appeal, but it wasn't clear exactly when.
"They clearly will not spare any expense to keep Mr. Assange in jail," his lawyer Mark Stephens told journalists outside the entrance to the City of Westminster Magistrates' Court in London. "This is really turning into a show trial."
Lawyer Gemma Lindfield, acting for Sweden, had asked the court to deny Assange bail, arguing on Tuesday that the allegations against him were serious, that he has only weak ties to Britain and he has "the means and ability to abscond."
Reminding the court that it had already labeled Assange "a flight risk," she argued that "nothing has changed since last week to allay the court's fears in this regard."
She also rejected attempts to link Assange's case with the work of WikiLeaks - which last month deeply angered US officials by beginning to publish its trove of 250,000 secret US diplomatic cables.
"This is not a case about WikiLeaks, rather a case about alleged serious offenses against two women," Lindfield told the court on Tuesday.
Celebrity supporters in the court - including socialite Jemima Khan and actress Bianca Jagger - and hundreds of pro-WikiLeaks protesters outside the building cheered at District Judge Howard Riddle's decision to grant Assange bail.
Under the ruling, Assange must wear an electronic tag, live at specific address in southern England, report to police every evening and observe two four-hour curfews each day in addition to putting up the bond.
In court last week, Lindfield said Assange is accused of rape, molestation and unlawful coercion by two women for separate incidents last August in Stockholm.
She said one had accused him of pinning her down and refusing to use a condom. A second woman says Assange had sex with her without a condom while he was a guest at her Stockholm home and she was asleep.
In Sweden, a person who has sex with an unconscious, drunk or sleeping person can be convicted of rape and sentenced to up to six years in prison.
Assange has not been charged in Sweden. His lawyers say the allegations stem from a dispute over "consensual but unprotected sex."
Several wealthy supporters - including filmmaker Michael Moore - have put up a total of £240,000 as a guarantee for Assange, his lawyers said.
Vaughan Smith, founder of the Frontline Club - a restaurant and forum for journalists in London - told the court on Tuesday that Assange was misunderstood.
Under the terms of his bail, Assange would be ordered to live at Ellingham Hall, Smith's 10-bedroom country mansion in Suffolk, southeastern England.
"The Julian Assange I know has a number of qualities. He's a very honorable person, hugely courageous, self-deprecatory, warm - none of the things you read about," Smith told the court.
Riddle said he had granted Assange bail because - unlike a week ago - he now had a verified address to live at and had cleared up confusion over when he arrived in Britain.
Assange's next court appearance was set for January 11, ahead of a full hearing on February 7 and 8.
Stephens said his client was "phlegmatic" about having to remain in jail.
Outside the court, Smith said Assange feared that the Swedish extradition case was an attempt to punish him for WikiLeaks' publication of the US diplomatic cables and that legal challenges from US authorities were coming in the future.
"What he fears is being hauled off to America to a dark room that doesn't have a key," Smith told reporters.
Demonstrators outside the court also believed Assange was being victimized.
"It is too much of a coincidence," said protester Alex Potterill, 33. "This is an attack on the valuable work of WikiLeaks. It is an attempt to gag a valuable source of information."
Assange's mother Christine, who was flown to Britain by Australian media outlets, watched the hearing nervously from a public gallery about 2 metres from her son's seat. She gave a huge smile as Riddle granted bail.
"I just want to thank everyone who's turned up to show their support and who's taken an interest," Christine Assange told The Associated Press as she waved to her son.
She was not in court later to hear that her reunion with her son had been thrown into doubt by the Swedish appeal.
