The medics have been in prison for seven years and had been sentenced to death by firing squad in May 2004 for infecting 426 children with the HIV virus in the northern city of Benghazi.
Bulgaria, the United States and the European Union have welcomed the decision, which is seen by some as a face-saving way out of the standoff over the case by Libyan leader Muammar Gaddafi.
The verdict comes after European and Libyan negotiators reached a deal that would see the West provide aid to the families of the infected children, around 50 of who have reportedly since died.
"The court has accepted the appeal of the Bulgarian nurses and ordered that a new trial will take place at the criminal court of Benghazi," said Supreme Court president Ali al-Alus said.
Libyan Justice Minister Ali Hasnawi told AFP that the new trial would be held "in one month" and that there would be "new judges".
None of the accused were present in the court on Sunday when lawyers for both sides presented their arguments.
Libya accused the six medics of deliberately infecting the children as part of an experiment, but the EU, US and human rights groups said Libya trumped up the charges to cover up poor hygiene standards at hospitals.
The six said they had been tortured to extract confessions.
In court, the judge said prosecutors agreed with defence lawyers that there were "irregularities" in the arrests and interrogations of the medical workers.
"The unfair death sentences were reversed... We hope that the swiftness and the effectiveness demonstrated by the Libyan court in the past days will help to solve the case as soon as possible," Bulgarian President Georgy Parvanov said.
The defendants' Libyan lawyer said he would ask for their release next month at the Benghazi hearing, and applauded the Supreme Court for recognising "procedural violations".
However parents and relatives of the infected children protested outside the court, shouting: "This is injustice, this is injustice".
They later took their protest to the centre of Tripoli, brandishing pictures of their dead children.
It remains unclear what the prospects are for the medics' eventual release, after the surprise announcement just days earlier by Bulgaria that it was creating a fund for AIDS-infected children in Libya.
Libyan media reports have suggested that the families of the children have agreed to drop their demands for the nurses to receive the death penalty in exchange for compensation.
The case has plagued Gaddafi's desire to rebuild ties with the West.
In 2003 Libya accepted responsibility for the 1988 bombing of a Pan Am jetliner over Scotland and agreed to compensate victims' families.
It also voluntarily gave up its nuclear program, and in response the US lifted a 23-year-old ban on travel to Libya.
But Washington has stressed that the medical workers' case is a key sticking point that must be resolved before relations are further normalised.