Aljazeera also thanked rights groups for support during the detention of their correspondent.
"Aljazeera takes this opportunity to extend its sincere appreciation to its viewers, regional and international human rights organisation, professional and civil societies and all those who supported Taysir, his family and Aljazeera," the channel said in a statement.
Aljazeera's correspondent Alluni had arrived at his Granada home, two days after a Spanish court ordered him moved from a maximum security cell to house arrest.
A frail and visibly fatigued Alluni emerged from a police van parked outside his Granada home at 3am (0200 GMT) after what he said was a gruelling five-hour journey from Madrid.
"I was strapped into a metal chair for five hours," he said.
While thanking his peers and the various organisations and individuals who laboured for his release, Alluni also criticised the Spanish government for his detention.
The Aljazeera correspondent says
he has lost faith in Spanish justice
"I no longer believe that the rule of law exists in this country (Spain)," he said.
"The trial will be highly politicised and a media affair. The prosecutor who ordered me re-jailed because he alleged I was a flight risk never presented any evidence to support his claim," Alluni said.
A Spanish judge had on Monday ordered Alluni released from jail and placed under mandatory house arrest pending his trial.
The release order was expected to be carried out late on Monday night or early on Tuesday, but had been set back after a series of delays.
Alluni is to appear before Spanish police every day while awaiting his trial. He is likely to be under house arrest during the course of the trial, Aljazeera has also learned.
Michael al-Kik, Aljazeera's correspondent in Granada, said the delays were due to security reasons - the Spanish authorities did not want to disclose information in what they perceive to be a top-security case.
He said once Alluni is under house arrest with a 24-hour guard, he will not be allowed to leave the premises even for medical treatment unless he has permission from the judge.
Syrian-born Alluni, a Spanish citizen, was first arrested in 2003 on suspicion of links with al-Qaida as part of an investigation into suspected Islamist operations in Spain.
He was then released due to chronic back problems and heart ailments but re-arrested in December 2004 when Spanish authorities feared he might flee the country.
Alluni's trial, and those of 18 others suspected of ties to al-Qaida, is expected to begin in late March or early April.