This was managed not so much by private industry as by a group of U.S. government agencies with ever shifting names like the War Production Board and the Office of Price Administration. In effect, between 1940-44 these agencies had turned a civilian market economy into a command economy where most decisions about what to produce were controlled by the U.S. government. This system had taken years to put together, starting in 1940 (before the war) and wasn't easily unravelled. Private business were not really able to resume producing civilian goods until the government permitted it and allocated or released raw materials to civilian uses.

However the urge to return to civilian production was strong. New cars hadn't been produced since 1942. Tires hadn't been available for years. Only essential clothing had been produced. New household appliances were unobtainable. The civilian economy had been getting along on worn out goods and everyone needed as well as wanted to replace them.

Additionally, a lot of people had savings. Servicemen had had little to spend their pay on for three years. Defense workers had been getting good wages, including many people who never had them before. Employment had been essentially at full from 1942-45, but there were few goods in stores that could be bought.

Luckily, the government agencies were well aware that the transition back to civilian a economy would be a difficult one. The experience of WWI had shown that a lack of planning in this transition would result in high inflation and massive unemployment. High inflation would result because there would be too many people with government paychecks or savings from the war years chasing the few civilian goods being produced by the economy as it transitioned to peacetime. Unemployment would be caused by millions of servicemen returning as well as defense workers being laid off.

Planning for a transition back to a civilian economy began in the late summer and fall of 1944 as the military situation suggested an end to the war. The War Production Board began to negotiate with the military for a reduction in munitions production even while the battles escalated in scope. Generally the military resisted all efforts to curtail military production until the war was completely won, but some industries received permission and resumed production early.

In any case, signals had been given to private firms to begin a transition to civilian production. Firms were well aware that high demand, savings (aka capital) and plentiful labor could mean a postwar environment where money could be made. Industrial machinery for civilian production was largely intact, or had even expanded during the war (e.g. rubber/tire production) because the government had made massive loans to industry, which had created new factories rather than repurposing old ones. So the machine tools and equipment needed for civilian production was still largely on hand. Additionally, the favorable terms of these loans (they enabled companies to give back the machine tools for military equipment in lieu of repayment) meant that US companies could end military production without taking a loss.

That being said, the transition was still messy. GDP fell sharply in 1946 and there was a modest degree of unemployment and inflation. Many smaller companies that had been pushed into war production folded or were bought by larger companies after the transition back to a market economy. The postwar economy was vastly different from the 1940 economy in so many ways.

Source: Klein, Maury. A Call to Arms: Mobilizing America for World War II Bloomsbury USA 2013