The Prime Minister said he was “very sad” to see youngsters absent from the streets and parks of Kyiv when he visited the Ukrainian capital last month, adding: “I cannot imagine how difficult this year must have been for you.”
But he said the children must bear two things in mind – that they should be “immensely proud” and they have “millions” of friends around the world.
Meanwhile, Mr Johnson resolved to “redouble efforts” to provide vital food and humanitarian aid to the Ukrainians, and ensure the country is able to export to the rest of the world.
The Prime Minister told Ukraine’s president, Volodymyr Zelensky, in a call on Sunday, that Britons are “1000%” behind his people, No 10 said.
In his letter to the Ukrainian children, Mr Johnson wrote: “When your president showed me around Kyiv last month, the absence of children and young people on the streets and in the parks made me feel very sad.
“Since the invasion many of you have been forced to flee your homes. You have left behind family, friends, pets, toys and all that is familiar, seeking refuge in underground stations, distant cities, even other countries. I cannot imagine how difficult this year must have been for you.”
Mr Johnson said the children should be proud of their country, their parents, their families, their soldiers, and “most of all” themselves.
“Many of you have seen or experienced things no child should have to witness,” he wrote.
“Yet, every day Ukrainian children are teaching all of us what it means to be strong and dignified, to hold your head high in even the toughest of times. I can think of no better role model for children and adults everywhere.”
The PM said the children may be separated from their friends at home but they have “millions of others all over the world”, including in the UK.
“We fly Ukrainian flags from our homes, offices, churches, shops and playgrounds, even from my own roof in Downing Street, where the windows are filled with sunflowers drawn by British children,” he wrote.
“Our young people are painting your flag in their classrooms and making blue and yellow bracelets in support of your country.”
He added: “I believe, like your president, that Ukraine is going to win this war. I hope with all my heart that, one day soon, you will be free to return to your homes, your schools, your families.
“And whatever happens, however long it takes, we in the UK will never forget you, and will always be proud to call you our friends.”
In his call with Mr Zelensky on Sunday, Mr Johnson was said to have paid tribute to the “incredible courage demonstrated by the president and his family in recent months”.
A Downing Street spokesman said: “The Prime Minister reiterated that the British people are 1000% behind the people of Ukraine.
“The leaders discussed (Vladimir) Putin’s despicable blockade of Odesa, Ukraine’s biggest shipping port. The Prime Minister resolved to redouble efforts to provide vital food and humanitarian aid to the people of Ukraine and ensure that the country was able to export to the rest of the world.
“The leaders agreed on the need for the international community to remain united in its condemnation of Putin’s barbarism. The Prime Minister said that every country had a duty to help Ukraine in their struggle for freedom, both now and in the long term.”
On Saturday, Cabinet ministers Liz Truss and Anne-Marie Trevelyan discussed the situation in Ukraine during meetings with a bipartisan US congressional delegation.
The talks followed the Foreign Secretary’s disclosure on Friday that she wants to see Moldova “equipped to Nato standard” to guard it against potential Russian aggression.
In an interview with The Telegraph, Ms Truss said the UK is discussing the prospect with its allies, given President Vladimir Putin has been “clear about his ambitions to create a greater Russia”.