Downing Street said he was moved to the unit on the advice of his medical team and was receiving "excellent care".
Mr Johnson has asked Foreign Secretary Dominic Raab to deputise "where necessary", a spokesman added.
The prime minister, 55, was admitted to St Thomas' Hospital with "persistent symptoms" on Sunday evening.
The Queen has been kept informed about Mr Johnson's health by No 10, according to Buckingham Palace.
World leaders - including US President Donald Trump and French President Emmanuel Macron - have expressed their support for Mr Johnson.
