The refugees also narrated to the UK minister the challenges they were facing in the camps.
Over 688,000 people have fled their homes in Rakhine State since August 25 last year, joining around 340,000 Rohingya who had previously fled.
The Foreign Secretary on Saturday toured a camp which is housing 500,000 refugees - equivalent to a city the size of Leicester, his office said in a statement.
He listened to their views, heard about their hopes for the future, and the conditions they believed needed to be put in place for any return to take place.
Johnson visited a UNICEF child-friendly site where he saw the efforts being made to keep young people safe. He sat down with some children on the site to talk about their drawings. He was also briefed on gender-based violence by caseworkers.
He left for Myanmar in the afternoon and will hold talks with de-facto leader Aung San Suu Kyi to discuss the crisis and press for the end to the suffering in Rakhine and the safe and voluntary return of the refugees.
"I pay tribute to the hospitality and compassion shown by the government of Bangladesh, who are facing an enormous challenge in providing humanitarian assistance to the Rohingya community.
"While I welcome steps by both the Burmese and Bangladeshi governments towards ensuring that these people can return home, it is vital that the Rohingya refugees must be allowed to their homes in Rakhine voluntarily, in safety and with dignity, under international oversight, and when the conditions in Burma are right."