Al Jazeera's Amr El-Kahky, reporting from Tripoli, said al-Megrahi received a warm welcome on his return home.
"Thousands of men, many of whom are teenagers, are holding up Libyan flags and banners welcoming al-Megrahi, happy to know that he's finally come home," he said.
"He was taken away in a car and it looks like his health is not so good because ... the celebration at a main square in the capital will proceed without al-Megrahi's presence."
The decision to release al-Megrahi was criticised by the US government and some victims' families who believe the Libyan, who was convicted of killing 270 people in the bombing, should remain behind bars.
Barack Obama, the US president, described the release as a "mistake" and said that al-Megrahi should be placed under house arrest on his return.
But MacAskill told reporters: "He [al-Megrahi] is a dying man; he is terminally ill. My decision is that he returns home to die."
Al-Megrahi, who has always protested his innocence, was released from Greenock prison in Scotland and escorted by a police convoy to Prestwick airport in Glasgow on Thursday afternoon.
"I have been faced with an appalling choice: to risk dying in prison in the hope that my name is cleared posthumously or to return home still carrying the weight of the guilty verdict, which will never now be lifted"
Abdel Basset al-Megrahi
In a statement following his release, al-Megrahi said: "I am obviously very relieved to be leaving my prison cell at last and returning to Libya, my homeland.
"The remaining days of my life are being lived under the shadow of the wrongness of my conviction.
"I have been faced with an appalling choice: to risk dying in prison in the hope that my name is cleared posthumously or to return home still carrying the weight of the guilty verdict, which will never now be lifted.
"The choice which I made is a matter of sorrow, disappointment and anger, which I fear I will never overcome."
Marwan Bishara, Al Jazeera's senior political analyst, said political motivations may have influenced the decision to release al-Megrahi.
"There's an understanding that with Libya now head of the African Union, and with it becoming the head of the UN General Assembly and a leading oil exporter, the idea of normalising relations with Libya in this kind of way is important and necessary.
"When it comes to national pride, Libya will do what it has to do, the US will say what it has to say, and I think in 48 hours a lot of us are going to forget about this."
MacAskill said the decision was made because Scottish law required that "justice be served, but mercy be shown".
Omar Turbi, an expert in US-Libyan relations, said that the release could also pose a dilemma for the Libyan authorities, given that in 2001 it accepted responsibility for the Lockerbie bombing.
"Will they move forward in their history and time, thinking, 'Okay, we want the world to think that we took revenge over America's [military] bombing of Tripoli in 1986, or shall we really take this stigma out of the world's view of us and clear it once and for all?'," he said.
"Libya is going to live with this stigma forever if it does not take a proactive step to clear its name."
Al-Megrahi was freed days after he dropped his second appeal against conviction, a condition necessary for the early release application to be considered.
|Abdel Basset al-Megrahi has repeatedly protested his innocence [AP]
The former agent lost an appeal in 2002 and last year failed to secure his release on the grounds that he was dying.
His lawyers began an appeal in May this year at a court in Edinburgh, saying the case against him was flawed.
The attack on December 21 1988 killed all 259 people on board and 11 on the ground.
Four years after al-Megrahi's conviction in 2001, Libya admitted responsibility and paid about $2.7bn in compensation to the families of those killed.
The move prompted the lifting of international sanctions against Libya and led to a restoration in diplomatic ties between Tripoli and the West.