Megrahi, the only person convicted over the 1988 bombing above Scotland which killed 270 people, died at his home in Libya on Sunday.
He was convicted by a special court in the Netherlands in 2001.
He was freed from a Scottish jail in 2009 on compassionate grounds as he was diagnosed with terminal cancer.
The BBC’s Rana Jawad in Tripoli says Megrahi’s body was transferred discreetly in an ambulance to the burial site, followed by a convoy of male relatives close behind.
The funeral was very much a private family affair and took place in the suburb of Janzour, where many other members of his family lay buried, our correspondent says.
“His pain is over now – he is with God,” said his brother Muhammad, quoted by the AFP news agency.
Another brother, Abdulhakim, said on Sunday that Megrahi’s health had deteriorated quickly and he died at home in Tripoli.
Megrahi’s release sparked the fury of many of the relatives of the victims of the Lockerbie bombing. The US – whose citizens accounted for 189 of the dead – also criticised the move.
But some of the relatives of those killed believe he was innocent.
In Libya, a spokesman for the National Transitional Council said Megrahi’s death would not close the Lockerbie file.
From the beginning, finding out the truth about Lockerbie was complicated by connections real and imagined, by skulduggery and intrigue, between rival powers in the Middle East, from Libya to Iran, and including the United States, says the BBC’s Middle East Editor Jeremy Bowen.
Unless some fresh evidence emerges, perhaps from the new Libya, the passing of the years means there might never be a version of the truth accepted by everyone affected by this tragic saga, he says.
Megrahi, a Libyan intelligence officer, always denied any responsibility for the bombing of Pan Am Flight 103 in December 1988.
It remains the deadliest terrorist incident ever to have taken place on British soil.
All 259 people aboard the plane, which was travelling from London to New York, were killed, along with 11 others on the ground.