He said Obama had added a handwritten message: "I hope we have future opportunities to collaborate."
"Little did I know that his staff had spoken to (German Chancellor) Angela Merkel about this," Stoltenberg wrote about the NATO job.
Months later, he met Obama adviser Karen Donfried, who described the president as "the world`s best campaign leader" who "is working for you."
On March 28, 2014, Stoltenberg was named the 13th NATO boss after winning support from the four most powerful NATO nations — the United States, Germany, Britain, and France.
Three years earlier, he was prime minister when 77 people were killed in a bombing and shooting rampage in Norway on July 22, 2011. When he was younger, Stoltenberg was actively engaged in the Labor Party`s youth summer camps on the island of Utoya where Norway`s worst mass killer, Anders Behring Breivik, gunned down 69 people after exploding a car bomb at government offices in Oslo that killed another eight people.
"It was brutal," Stoltenberg wrote about slayings at the camp he knew so well.
Norway`s prime minister from 2000-2001 and from 2005-2013, he was named special envoy on climate change in December 2013 by U.N. Secretary-General Ban Ki-moon.
But when pondering whether to take the NATO job, he remembered that international politics had taught him that "the big nations that decide most of it," not the head of the organizations.
He described the NATO job "as a thrilling task" but admitted that as a young politician he had defended the youth branch`s stance that Norway should leave NATO. It did not.
Stoltenberg`s news conference for the book was postponed from Friday to Saturday to let him attend Shimon Peres` funeral.