Mr Johnson met Somalian President Mohamed Abdullahi Mohamed, who was elected last month, to discuss the situation.
He told the president: “It’s a shame that you’re facing the problems that you are, particularly drought and the risk of starvation.
“I think we’re moving fast to try to tackle that this time round and the UK Government has pledged £110m to try to kick-start that work and make sure we get supplies to those who need it.
“Drought, a problem like that, is fundamentally something that is caused by human agency or lack of human agency, poor government, corruption, the struggle that you have against terrorism and there we are very proud to be supporting you as well.”
Mr Johnson also saw demonstrations of the training provided by the British military in the country.
They also discussed security in the country, where terror group al Shabaab continues to carry out attacks.
The Disasters Emergency Committee’s (DEC) East Africa Food Crisis Appeal is hoping to bring aid to more than 16 million people in the region “on the brink of starvation and in urgent need of food, water and medical treatment”.
Money raised by the DEC appeal will go to those affected in Somalia, Kenya, Ethiopia and South Sudan, with the Government pledging to match public donations up to £5m.
The Queen is also making a personal donation to the appeal, a Buckingham Palace spokesman confirmed.
Sir Mo, who spent his early childhood in some of the worst affected areas of Somalia, said he was “completely devastated” by the crisis.
He said: “As a father of four, it hurts to see children without food and water, but this is a reality being faced by parents in East Africa right now.”
The UN children’s agency has warned that 1.4 million severely malnourished children could die this year in Somalia, Nigeria, South Sudan and Yemen.
In February, the UN formally declared a famine in parts of South Sudan – the first time in six years such an announcement has been made.
DEC chief executive Saleh Saeed said: “We are hearing that families are so desperate for food that they are resorting to eating leaves to survive.
“This is something no family should have to endure. Unless we act now the number of deaths will drastically increase.”