Miliband, whose violinist wife Louise is an American citizen, adopted a boy named Jacob, his office said, without giving further details.
The couple are already the adoptive parents of two-year-old Isaac, who was born in the United States in December 2004.
"David and Louise Miliband are pleased to announce the adoption of their second son, Jacob," Miliband's office said in a statement. "They are delighted by the new arrival and Mr. Miliband will now be taking a period of leave."
Miliband's office would not give details about where the family's second child is from.
Miliband had been due to attend a meeting Monday with Saudi foreign minister Prince Saud Al-Faisal, the first event of a state visit by King Abdullah of Saudi Arabia.
Foreign Office Minister Kim Howells minister replaced Miliband, but officials said Prince Saud Al-Faisal had also decided not to attend the scheduled meeting.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
This problem is not limited to the situation with the "whale prison" in Russia's Far East, because many people buy tickets to go to oceanariums and turn a blind eye to the problem