The British embassy in the US capital had originally said Cameron would not have time to meet the lawmakers as he had a full schedule, and would instead ask British Ambassador Nigel Sheinwald to see them.
But his spokesman later said the prime minister, on his first visit to Washington since taking office in May, had changed his plans and would invite the senators for a discussion later Tuesday at the British ambassador's residence.
"The prime minister recognises the strength of feeling and knows how important it is to reassure the families of the victims," said the spokesman.
"We are happy to see them face to face and find time in the diary."
Democratic Senators Chuck Schumer and Kirsten Gillibrand of New York and Frank Lautenberg and Robert Menendez of New Jersey wrote a letter to Cameron Monday asking to meet with him to discuss the Lockerbie case.
The lawmakers said they hoped to discuss "what we can all do to provide greater transparency into the circumstances surrounding the release, address the injustice, and ensure that a similar mistake is not repeated."
The quartet said US Secretary of State Hillary Clinton had advised them that she had requested Cameron's government to "review the facts and circumstances" leading up to the release of Libyan Abdelbaset Ali Mohmet al-Megrahi.
Megrahi, the only person convicted of the 1988 bombing of a US Pan Am jumbo jet over the Scottish town of Lockerbie in which 270 people were killed, was freed from a Scottish jail last year.
He had been sentenced to life imprisonment but was freed in August on compassionate grounds after doctors said he had only three months left to live. Reports have since emerged that he could live another 10 years.
Menendez earlier described Cameron's initial refusal to meet with him and his fellow senators as "disappointing", adding that "it is critical for us to get the full story from the British government."
Source: AFP Global Edition