Stoltenberg told a press conference after news of his appointment that it was crucial the 28-nation transatlantic alliance kept up military spending.
"We are neighbour to a superpower (Russia) with increasing military capacity and increasing military activity in the Northern regions, but also along the borders with Ukraine," he said.
"This only underlines the importance of having both sufficient budgetary allocations to the military forces but also an effective structure of the military."
An economist by training and a radical opponent of the alliance in his youth, Stoltenberg takes the helm as Europe worries over a Russian build-up on its eastern fringe after Moscow's takeover of Crimea.
His appointment came quicker than anticipated, the decision made "without opposition" after a comfortable consensus grew around Stoltenberg, a diplomatic source said.
Stoltenberg was initially approached about the position in January but did not accept immediately, he said, claiming he wanted to be sure that the NATO members were in favour of his appointment.
He also thought it unlikely that NATO would call on a Norwegian after the alliance had been led by the Dane Rasmussen in recent years.
The White House said it welcomed the appointment. In a statement, Washington said: "Mr. Stoltenberg is a proven leader with a demonstrated commitment to the transatlantic Alliance. "We are confident he is the best person to ensure the continued strength and unity of the NATO Alliance."
Stoltenberg, who is 55, was the only candidate for the job and leaders of NATO's main powers, including US President Barack Obama and German Chancellor Angela Merkel, had all rallied around the former prime minister in recent weeks.
He was also praised by the man he will be replacing.
"I've known Jens Stoltenberg for many years and I know he's the right man to build on NATO's record of strength and success," said Rasmussen on Twitter.
In almost a decade leading the Norwegian government, Stoltenberg, who is the country's Labour Party chief, became known as a consensus maker, giving him some of the right credentials to maintain good relations with Russia.
Though he never had any particular fondness for defence or security matters, his experience as premier left him with a strong international network and honed his skills as a cross-border negotiator.
"This is a key strength given the Ukrainian crisis," a diplomat said in Brussels, where the NATO headquarters is located.
His arrival to NATO comes at a pivotal moment, with fears growing over Russia's resurgence as a military power to contend with, more than two decades after the end of the Cold War.
Created in the years following World War II as a western bulwark against the Soviets, NATO is now on the frontlines of the crisis in the Ukraine, though the former Soviet state is not a member of the alliance.
"We do not seek confrontation but we will not waiver if challenged," Rasmussen said after a brief meeting with Obama in Brussels this week.
During the visit, the US president said that "NATO nations never stand alone" and underlined that the alliance was now patrolling the skies over the Baltics, and had reinforced its presence in Poland.
Polish foreign minister Radoslaw Sikorski, who was also rumoured for the NATO job, congratulated Stoltenberg on his nomination.
Sikorski said he was sure the new NATO head "will strive for equal security for all members," in an oblique recommendation to the alliance to remember its eastern-most members on the borders with Russia.
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Stoltenberg is set to take office on October 1, after an alliance summit in Cardiff.
At that time, the alliance should be in the final stages of pulling out the last of its combat forces in Afghanistan, where NATO troops have been fighting the Taliban for over a decade.
Before the Ukraine crisis, there were fears that the alliance would struggle to find a new direction after the Afghanistan exit, especially as Western powers, looking to shore up government finances, slashed defence spending.
"Recent events in Ukraine have underlined that, even once we complete our mission in Afghanistan, there will be new challenges to respond to," British Prime Minister David Cameron said on Friday.
With this new sense of purpose, Stoltenberg, the former pacifist protester, will have to persuade the alliance's European powers to reverse the defence spending cuts.
During his Brussels visit, Obama also urged European governments to not abandon defence and remember their historic responsibility, especially with Russia's potential return as a threat.
"We must never forget that we are heirs to a struggle for freedom," Obama said.