Moore, who flew from Baghdad via Amman in Jordan, was met by officials before being driven to be reunited with his family off-base.
His father, Graeme Moore, said he was "absolutely delighted" at his return, saying: "I want to give him a big hug when I see him... Me and his friends can't wait to see him and it's just a massive relief to get him home."
Moore's step-parents Fran and Pauline Sweeney appealed for privacy.
"We are thrilled to have Peter back safely. We have a lot of catching up to do and would like to have time with Peter on our own," they said.
Moore is reportedly going to be sent to a safe house for assessments by doctors and psychiatrists and help in readjusting to normal life.
Following his release, the BBC quoted him as saying he had been subjected to "rough treatment" while in captivity, but he had been well treated in the final six months, including being given access to a television and Playstation.
Relatives of Moore and of the guards captured with him have meanwhile spoken of their anger at the British government's handling of the matter.
The bodies of three bodyguards -- Alec MacLachlan, 30, Jason Swindlehurst, 38, and Jason Creswell, 39 -- were handed over to British officials last year. A fourth, Alan McMenemy, 34, is also believed to be dead.
McMenemy's father Dennis accused the Foreign Office of "deceit, lies and cover-up" while Moore's mother Avril Sweeney said the government had "never told the truth", the Guardian reported.
The paper said Thursday that Iran's Revolutionary Guard led the kidnap operation and took the five to Iran within a day of their abduction.
General David Petraeus, the US regional military commander, reiterated to reporters in Baghdad Friday that Moore spent "at the very least" part of his time in captivity in Iran.
"That is based on an intelligence assessment and obviously I've not had a chance to hear it, certainly not to talk to him, but nor to hear anything that he has said," Petraeus said.
Some commentators said a deal may have been done to free Moore after Qais al-Khazali, leader of the group which captured the Britons from a government building in Baghdad, was recently transferred from US to Iraqi custody.
Graeme Moore said he believed this is what had happened.
"About four weeks ago, I got a tip that there had been secret meetings between the kidnappers and the Americans regarding al-Khazali," he said, without revealing his source.
"I couldn't find out any more progress of the meetings as it was all being kept hush-hush. The whole thing was kept very secret to stop the Foreign Office messing it up."
The Foreign Office denied any deal was done, saying the United States transferred al-Khazali into Iraqi custody under the terms of a bilateral status of forces agreement.
"Separately, the government of Iraq is carrying out a process of reconciliation with groups willing to renounce violence and enter the political mainstream," it said in a statement.
"Since holding hostages is incompatible with reconciliation, we judge that progress on the wider reconciliation effort will benefit hostages held in Iraq.
"There has been no prisoner exchange deal in the case of Peter Moore."
Britain and Iran have also played down reports of a link to Iran.