Mr Miliband and his wife are said to be delighted

A spokesman said he and his wife Louise were "delighted" with newborn Jacob and said he would be taking some leave.

The couple have another adopted son, two-year-old Isaac, who was born in the US in December 2004.

Mr Miliband had been due to launch a conference with his Saudi counterpart Prince Saud al-Faisal, but his place was taken by Kim Howells.

It is understood that he was in the US for Jacob's birth and is in the process of returning to Britain. Mrs Miliband grew up in the US and went to university there.

In a statement his office said: "David and Louise Miliband are pleased to announce the adoption of their second son, Jacob.

"They are delighted by the new arrival and Mr Miliband will now be taking a period of leave.

"They ask the media to respect their privacy during this time."

Prince Saud also did not attend the conference - officials said it was a matter of protocol as his British counterpart would not be speaking.