The paper reports that Merkel put forward Stoltenberg's name shortly after his centre-left coalition was ousted from government in September.
Stoltenberg then spent months discussing the role with US Secretary of State John Kerry and his security advisor Susan E. Rice, while he was in New York over the winter, ostensibly in his role as UN Special Envoy for Climate Change.
According to the paper, Merkel made her proposal directly to President Barack Obama, who apparently agreed that Stoltenberg was a good choice for the role.
Denmark's Anders Fogh Rasmussen is set to leave the post in September.
Until a report this week in Italy's La Repubblica newspaper, it was generally thought that the next appointment would go to someone from outside Scandinavia, with Italy's former Foreign Minister Franco Frattini, Britain's Defence Secretary Philip Hammond, and the Polish Foreign Minister Radoslaw Sikorski all names seen as being in the running.
Nato has been led by a European ever since it was founded in 1949, but news agency NTB notes that there are otherwise few selection rules or guidelines.