The elevation of Andy Jassy to become Inc.’s next chief executive is one of the clearest signs yet that fortunes in the tech industry are increasingly made in the cloud.

Mr. Jassy was instrumental in helping to transform the online retailing giant he joined in 1997 into a juggernaut in cloud-computing, the business of renting servers and software to customers largely on a pay-as-you-go model. It is a market that could top $300 billion globally this year, according to research firm Gartner Inc., and pits Amazon against tech giants like Microsoft Corp. and Alphabet Inc.’s Google.

The battle for the cloud is playing out across industries—from videogames and cars to space—and companies large and small.

For Amazon, cloud computing has been a booming business that is massively lucrative. Amazon Web Services, or AWS,  generated little more than 10% of Amazon’s total sales in the final quarter of last year but yielded more than half the company’s operating profit in the period. AWS revenue advanced 28% over those three months from the previous year to $12.7 billion, and its operating profit was $3.6 billion.

For executives, the cloud is increasingly becoming a stepping-stone at tech companies. Microsoft CEO Satya Nadella ran the software giant’s cloud business before being elevated to the top job in 2014. International Business Machines Corp. last year turned to its cloud chief when it came to naming a new CEO to help revive growth.

Mr. Jassy’s appointment—he replaces Amazon founder Jeff Bezos as CEO in the third quarter—is noteworthy because Mr. Jassy is taking over not just a tech company but one of the world’s largest retailers.

“This speaks to how important the cloud is becoming to our economy,” said Rishi Jaluria, an analyst for investment research firm D.A. Davidson & Co. “With Andy Jassy in charge of all of Amazon, it shows how the company wants to bring that DNA at the core of AWS to all of Amazon.” Amazon Web Services generates a smallshare of total revenue but more than 50% ofoperating profit.

The breadth of tools that Amazon and others now offer via the cloud has exploded as companies across industries collect more data on their products, customers and employees. Cloud vendors now provide applications to, for instance, help manage and analyze that trove of information, increasingly using artificial-intelligence software to automate those processes.

Investors are rewarding businesses that have embraced cloud-computing, and they have taken a dimmer view of those struggling to adapt.

Snowflake Inc., a company that offers tools to help companies manage their data across multiple clouds, went public last year in a blockbuster offering. Shares, down from their December highs, are up about 18% since their debut. Data-analytics startup Databricks Inc. recently raised $1 billion, giving the San Francisco-based company a $28 billion valuation. Inc., launched more than two decades ago as a cloud-based software company, has grown into one of America’s biggest providers of enterprise tools, using its rising fortunes to help fund deals including an agreement late last year to buy cloud-based workplace-collaboration software provider Slack Technologies Inc.

Companies that were slow to embrace the cloud are trying to catch up. Larry Ellison, the founder and executive chairman of database provider Oracle Corp., once dismissed cloud computing as a fad. In recent years Oracle has ramped up its cloud efforts and poached staff from AWS. Mr. Ellison now regularly trumpets the company’s cloud exploits on earnings calls and last year landed popular videoconference company Zoom Video Communications Inc. as a cloud customer to burnish Oracle’s credentials.

Early in the pandemic, the multiyear growth run in cloud spending seemed at risk as many American businesses hunkered down. Salesforce cut its full-year outlook as it provided some struggling customers a payment holiday. IBM in April withdrew its full-year guidance.

But reality played out differently. The pandemic has supercharged the cloud as businesses rushed to adopt tools to help them cope with remote working and other challenges during the health crisis. Before the pandemic, Microsoft’s Azure cloud had seen its growth rate slow as it gained scale. That reversed in recent months. Azure sales increased 50% year-over-year in the December quarter, up from 48% during the previous quarter.

“What we have witnessed over the past year is the dawn of a second wave of digital transformation sweeping every company and every industry,” Mr. Nadella said last month.

Amazon is the clear leader in the cloud by sales, though companies calculate revenue generated through those activities differently. AWS had a market share of around 34% at the end of last year, according to Synergy Research Group. Microsoft was second with a 20% slice but has been narrowing the gap, according to Synergy.

Amazon’s rise in cloud hasn’t been without challenges. In addition to the increased competition, some retailers—like Walmart Inc. —are shunning AWS and teaming with rivals because of concerns about giving Amazon more business and might.

The cloud also is increasingly a political minefield as it becomes more central in daily life. Amazon was caught last month in the difficult question of what content to allow or bar on its platform. AWS kicked right-wing social network Parler off its cloud, saying the platform didn’t adequately police its content and failed to remove material that violated Amazon’s terms of service. Parler is suing Amazon over that move.

When a U.S. House panel issued a report last year on antitrust concerns around big tech companies, it said AWS provides key infrastructure for businesses that compete with Amazon. “This creates the potential for a conflict of interest where cloud customers are forced to consider patronizing a competitor, as opposed to selecting the best technology for their business,” the committee wrote. Amazon has said it doesn’t use AWS to give its retail arm an advantage.

Amazon also drew lawmakers’ attention when a former employee was arrested in 2019 for orchestrating the hack of Capital One Financial Corp. , one of the biggest-ever bank-data thefts.