Mr Brokenshire said on Wednesday he is standing down from the Government to “focus on restoring my health”, having been diagnosed with the condition two years ago.
In a letter, Mr Brokenshire thanked the Prime Minister for his support during the treatment and praised the “truly amazing” medics who have been working with him.
“My recovery from treatment and return to full duties is, however, taking longer than anticipated,” he wrote.
“Given my responsibilities to the public, the Government and to Parliament, I have therefore concluded that it is best that I stand down from my ministerial role and focus on restoring my health.”
He said he hopes to be able to “serve again in some way in the future”.
Mr Johnson responded by offering his full support and to wish him a “speedy return to full health”.
The Prime Minister added: “I understand entirely your need to step down from your role but look forward to welcoming you back as soon as possible.”