The inquiry, announced in London, will investigate 25 drone strikes in Pakistan, Yemen, Somalia, Afghanistan and the Palestinian territories.
British lawyer Ben Emmerson will investigate the extent of civilian casualties, the identity of the targets, and whether the attacks could constitute war crimes.
Mr Emmerson said there has been an exponential rise in the use of drone technology because of the low cost of their deployment, both economically and in terms of risk to the lives of service personnel.
While most attacks with unmanned aerial vehicles have been by the United States, Britain and Israel have also used them and dozens more countries are believed to possess the technology.
But Mr Emmerson also said he would not single out the biggest users.
"The plain fact is that this technology is here to stay, and its use in theatres of conflict is a reality with which the world must contend," Mr Emmerson said.
"It is therefore imperative that appropriate legal and operational structures are urgently put in place to regulate its use in a manner that complies with the requirements of international law."
Criticism of drone strikes centres on the number of civilians killed and the fact that they are launched across sovereign states' borders so frequently - far more than conventional attacks by piloted aircraft.
Retired US General Stanley McChrystal, who authored the US counter-insurgency strategy in Afghanistan, earlier this month warned against overusing drones, which have provoked angry demonstrations in Pakistan.
Data collected by the Bureau of Investigative Journalism indicates 2,600-3,404 Pakistanis have been killed by drones, of which 473-889 were reported to be civilians.
The UN's Human Rights Council asked Mr Emmerson to start an investigation following requests by countries including Pakistan, Russia and China to look into drone attacks.
Mr Emmerson said that he did not expect the inquiry to result in a "dossier of evidence" that would directly point to legal liability, but that results would help support the relevant states' own independent investigations.
He also said Britain's Ministry of Defence had agreed to fully cooperate and he was optimistic he would receive good cooperation from US and Pakistani governments.
Hina Shamsi, director of the American Civil Liberties Union's National Security project said he welcomed the investigation "in the hopes that global pressure will bring the US back into line with international law requirements that strictly limit the use of lethal force".
"To date, there has been an abysmal lack of transparency and no accountability for the US government's ever-expanding targeted killing program," Ms Shamsi said.
The report and recommendations will be presented at the UN General Assembly in New York in October this year.