The country's de facto leader, Nobel peace laureate Aung San Suu Kyi, has faced worldwide condemnation for her apparent inaction in the face of the widely alleged reports of atrocities committed against the Rohingya, which the United Nations says might amount to genocide.
Mr Johnson's intervention came after he spent Saturday touring a refugee camp in Cox's Bazar, on the south east coast of Bangladesh.
The United Nations has described the exodus of Rohingya as a "textbook example of ethnic cleansing".
The killings of 10 Rohingya men occurred in the village of Inn Din in September a year ago and the bodies were buried in a mass grave after they were hacked to death or shot and killed by Buddhist neighbours and Myanmar soldiers.
Action will be taken against 10 members of Myanmar's security forces in connection with the killing of captured Rohingya Muslims in Rakhine state, a government spokesman said on Sunday.
Mr Johnson will now fly to Myanmar, where he is due to meet de facto leader Aung San Suu Kyi on Sunday.
Rohingya refugees are seen at a refugee camp at no-man's land at the Bangladesh Myanmar border in Cox's Bazar Bangladesh Jan 12 2018. Reuters
But aid agencies have joined the refugees themselves in expressing fears about the conditions and their rights and safety upon their return.
"I underlined the importance of the Burmese authorities carrying out a full and independent investigation into the violence in Rakhine, and to hold to account those responsible for human rights violations", Johnson said in a statement, using the alternative name for Myanmar, released after the meeting and a brief trip to northern Rakhine.
Britain's foreign secretary has said it is "vital" that Rohingya refugees in Bangladesh should be allowed to return to Myanmar "in safety and with dignity".
"This once more attests to the need for a full and thorough investigation by the authorities of all violence in Rakhine State and attacks on the various communities there", United Nations spokesman Farhan Haq told reporters in NY.
The UK's foreign secretary told reporters the charred homes of devastated Rohingya villages were like nothing he had seen before in his life, after visiting refugee camps in Bangladesh and northern Rakhine state in Myanmar.
He will go on to Bangkok, Thailand, for talks with Thai Prime Minister Prayut Chan-o-cha.
FireEye, Inc. (NASDAQ:FEYE) To Report Earnings
Following the completion of the transaction, the director now directly owns 7,099 shares in the company, valued at $96,333.43. The company had revenue of $202.30 million for the quarter, compared to the consensus estimate of $193.74 million.