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 behavior of the Russian inspector satellite, which was launched in the autumn of 2017, puzzles military officials in the United States
When the bill was submitted to Congress on August 2, the reason for imposing the new sanctions on Russia was based on Russia's alleged interference in the US presidential election in 2016, but then something clicked