Kremlin spokesman Dmitry Peskov said the change made sense because Russia was approaching a situation like the Soviet Union in the mid-1980s, when the military and law enforcement authorities accounted for 7.4% of gross domestic product (GDP).
That, said Peskov, meant it was vital to ensure such spending aligned with and was better integrated into the country's overall economy, which was why Putin now wanted a civilian economist in the defence ministry job.
"The one who is more open to innovations is the one who will be victorious on the battlefield," Peskov said.
Belousov, a former economy minister known to be very close to Putin, shares the Russian leader's vision of rebuilding a strong state, and has also worked with Putin's top technocrats who want greater innovation and are open to new ideas.
Belousov has played an important role in overseeing Russia's drone programme.
The shake-up, which caught the elite off-guard, indicates Putin is doubling down on the Ukraine war and wants to harness more of Russia's economy for the war after the West sought, but failed so far, to sink the economy with sanctions.
ECONOMIC WAR
Russia's economists have so far largely ensured economic stability and growth despite the toughest sanctions ever imposed on a major economy, even though the failings of the Russian military were laid bare shortly after the invasion.
"The proposal to appoint one of the main court economists and the main state minister in the economic bloc to head the Defence Ministry may mean that Putin is planning to win the war with the defence industry plants and international markets," said Alexander Baunov, a former Russian diplomat who is now a senior fellow at the Carnegie Russia Eurasia Center.
"The winning strategy in this case will not be mobilisations and breakthroughs, but slow pressure on Ukraine with the superior power of the Russian military-industrial complex and the economy as a whole, which, apparently, is supposed to be made to work more effectively for the front and rear."
Putin's move, though unexpected, preserves balance at the top of the complex system of personal loyalties that make up the current political system.
The shake-up gives Shoigu a job that is technically regarded as senior to his defence ministry role, ensuring continuity and saving Shoigu's face. Valery Gerasimov, the chief of Russia's General Staff and someone with a more hands-on role when it comes to directing the war, will remain in post.
Shoigu was heavily criticised by Russian military bloggers for a series of retreats the Russian military was forced to make in 2022. Yevgeny Prigozhin, the leader of the Wagner mercenary group and one of Shoigu's fiercest critics, led an abortive mutiny he hoped would topple Shoigu last year before agreeing to call it off. Prigozhin was later killed in a plane crash.
Mark Galeotti, director of the London-based Mayak Intelligence consultancy, said the defence minister's job in Russia at a time of war was to ensure the military had everything it needed, while Gerasimov's job was the "key one" as he now reported directly to Putin, the commander-in-chief.
"In that context, having an economist, someone who has been speaking about the need to basically subordinate much of the economy to the needs of the defence sector, makes a certain amount of sense. It is now essentially a financial administrator's job and Belousov can do that," said Galeotti.
The change is likely to be seen as an attempt by Putin to subject defence spending to greater scrutiny to ensure funds are effectively spent after a Shoigu ally and deputy defence minister, Timur Ivanov, was accused by state prosecutors of taking kickbacks worth nearly $11 million.
Putin left Alexander Bortnikov and Sergei Naryshkin, the chiefs of the Federal Security Service (FSB) and the Foreign Intelligence Service (SVR), in their posts.
Sergei Lavrov, the country's veteran foreign minister, will also stay in his job, the Kremlin said.