The meeting followed Johnson's visit to a refugee camp in Bangladesh's Cox's Bazar district, where almost 700,000 Rohingya have sought sanctuary after fleeing a Myanmar army crackdown launched in northern Rakhine last August.
Bo, who was at a Vatican conference on human trafficking, again defended Myanmar civilian leader Aung Sung Suu Kyi, saying she has no constitutional right to speak out against the military.
Doctors Without Borders (Medecins Sans Frontieres) estimates 6,700 Rohingya died in the first month of violence.
A Reuters investigation into the killing of Rohingya Muslims in Myanmar prompted a demand from Washington for a credible probe into the bloodshed there and calls for the release of two journalists who were arrested while working on the report.
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. But the Nobel laureate has refused to change tack.
Two Reuters journalists now in detention in Myanmar were arrested by authorities there because they were investigating a mass execution of minority Rohingya Muslims in the country's Rakhine state, the news agency has said.
"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". They will visit Rohingya camps and meet global NGOs working in the Rakhine State, Myanmar civil society organisations, religious and political leaders as well as the media.
Mr Johnson will later be taken on a tour of Rakhine State - the area the refugees fled from - by the Myanmar military and will also meet the chair of the Advisory Board on the Rakhine Advisory Commission, Surakiart Sathirathai.
A month after the journalists were detained, Myanmar's army issued a rare statement taking responsibility for the deaths but claimed that those killed were "Bengali terrorists", reflecting the regime's official stance that the Rohingya are interlopers from neighboring Bangladesh.
He will go on to Bangkok, Thailand, for talks with Thai Prime Minister Prayut Chan-o-cha.