The White House was due to announce a series of measures aimed at moving the controversial US drone killings programme out of the "legal shadows" on Thursday.

In a major counter-terrorism speech billed as marking the end of an unfettered "war" on terror, Barack Obama was expected to reveal that he will move responsibility for future drone operations from the CIA to the Pentagon so they can be more closely monitored by Congress.

A more limited range of strikes in countries such as Yemen are likely to be carried out by the US military working within a new set of legal guidelines agreed by Obama this week, giving greater clarification on how and when officials can target suspected terrorists operating abroad.

Attorney general Eric Holder told congressional leaders in a letter on Wednesday that they would be briefed in private on whether future drone attacks on suspected terrorists passed the new legal threshold.

Both the White House and the CIA declined to comment on details of the policy ahead of the speech but government sources told the Guardian they would add to existing congressional oversight measures in place. Until recently the administration did not even publicly admit the existence of the drone programme.

Human rights campaigners have cautiously welcomed the attempt to bring US drone warfare policy into the open, but called on President Obama to publish the new legal tests that he was due to announce later on Thursday.

Dixon Osburn, a director at Human Rights First, said: "On its own, it is not clear that taking things away from the CIA makes a difference – the special operations command at the Pentagon is also secret – but at least the military are schooled in the rules of war."

"It looks like Obama is trying to return his counter-terrorism strategy to something that operates within the law. We want to know what that legal framework is though."

Earlier, the White House marked this new effort to draw a line under the controversial drone-strike policy by admitting for the first time that four American citizens were among those killed by its covert attacks in Yemen and Pakistan since 2009.

In a letter to congressional leaders sent on Wednesday, attorney general Eric Holder Holder claimed one of the US citizens killed, Anwar al-Awlaki, was chief of external operations for al-Qaida in the Arabian Peninsula (Aqap) and had been involved in plots to blow up aircraft over US soil.

However, Holder said three others killed by drones – Samir Khan, Abdul Rahman Anwar al-Awlaki and Jude Kenan – were not "specifically targeted". The second of these victims, Anwar al-Awlaki's son, is said by campaigners to have been 16 when he died in Yemen in 2011.

The Bureau of Investigative Journalism estimates that between 240 and 347 people have been killed in total by confirmed US drone strikes in Yemen since 2002, with a further 2,541 to 3,533 killed by CIA drones in Pakistan.

"The president will soon be speaking publicly in greater detail about our counter-terrorism operations and the legal and policy framework," Holder told 22 senior members of Congress in Wednesday's letter.

"This week the president approved a document that institutionalises the administration's exacting standards and processes for reviewing and approving operations to capture or use lethal force against terrorist targets outside the United States and areas of active hostilities."

The attorney general said this document would remain classified, but relevant congressional committees would be briefed on its contents. No further details were given of other killings in the five-page letter.

White House spokesman Jay Carney said Obama would also outline his renewed attempt to shut the Guantánamo Bay detention centre in the speech, and seek to explain why previous efforts had failed.

The White House said Thursday's speech will cover "broad counter-terrorism policy, including military, diplomatic, intelligence, and legal efforts".

"[Obama] will review the state of the threats that we face, particularly as the al-Qaida core has weakened but new dangers have emerged," it added. "He will discuss the policy and legal framework under which we take action against terrorist threats, including the use of drones.

"He will review our detention policy and efforts to close the detention facility at Guantánamo Bay. And he will frame the future of our efforts against al-Qaida, its affiliates and its adherents."