The agreement came after David Cameron and General Prayuth Chan-ocha discussed controversy surrounding the Thai-led investigation of the killings at a summit in Milan.
The British officers are expected to seek independent checks of DNA samples seen as key to the case against two Burmese men accused of the crime.
They are also expected to examine claims by the two migrant workers that they have been mistreated by the Thai authorities.
Mr Miller, 24, and Ms Witheridge, 23, were found dead last month on a beach on Koh Tao, an island in Thailand’s Surat Thani province.
Court proceedings have reportedly started against the two suspects amid international concern about the investigation, including from the Foreign Office and human rights groups.
The Thai leader had previously rejected offers of help and insisted the UK no longer had “any more doubts” about the quality of the investigation following ambassador-level talks.
But sources said he agreed to a British police delegation when pressed on the issue by the Prime Minister at the Asia Europe Meeting in Italy.
A diplomatic source said: “Obviously it is for the Thai authorities to lead and carry out that judicial process.
“But it is important that it is fair and transparent and that both of the families can be reassured that it is the murderers that have been brought to justice.
“What the PM secured this morning was agreement from the Thai PM that we can send some British police investigators to Koh Tao to work with the Royal Thai Police on this.”
The Burmese men who have been charged with the killings were paraded in front of the media after apparently making confessions which were later withdrawn.
The pair have reportedly been charged with three offences – conspiracy to murder, conspiracy to rape and robbery.
Thai police denied reports that the Burmese embassy had formally retracted their confessions amid claims the pair were tortured.