Then everything moved online. More than 500,000 doctors’ offices, farmers markets and other businesses migrated to online payments and used Stripe to do it. As people worked out at home, redecorated or both, Stripe customers such as

Peloton Interactive Inc.

and

Wayfair Inc.

enjoyed blockbuster sales.

Stripe’s revenue last year rose nearly 70%, to about $7.4 billion, according to people with knowledge of the company’s finances. Other startups might have flashier apps or more recognized brands, but Stripe showed that it is better to be a workhorse than a show pony.

Now sitting atop a $95 billion valuation—the highest for a private Silicon Valley company, according to data firm PitchBook—Stripe is bulking up overseas, preparing to go public and working to build a one-stop financial supermarket for the internet economy.

Dhivya Suryadevara,

Stripe’s finance chief, joined last year after holding the same position at

General Motors Co.

She expects Stripe’s growth to continue. “I was quite blown away by just how much opportunity still exists,” she said.

The company has two major trends in its favor: Investors view Stripe as an index of sorts for all of Silicon Valley, because it processes payments for plenty of fellow startups and tech companies—and Silicon Valley has thrived almost since the pandemic began. 

What’s more, people have embraced online shopping and are expected to keep at it even when Covid-19 fades. The pandemic accelerated the shift to e-commerce by two years, with online retail sales in the U.S. increasing in 2020 by nearly one-third to $795 billion, according to research firm eMarketer.

Irish brothers

Patrick

and

John Collison

launched Stripe around 2010 after dropping out of the Massachusetts Institute of Technology and Harvard University, respectively. Frustrated with the experience of getting their earlier business ventures approved for credit-card-processing accounts, the Collisons decided to build a solution themselves.

At the time, there was a perception that online payments were a solved problem. Dot-com darling PayPal Holdings Inc. had been around for more than a decade, but after it sold itself to

eBay Inc.,

the company primarily catered to merchants there.

Stripe started out by working with a group particularly neglected by banks: other startups. As customers such as Instacart Inc. and

DoorDash Inc.

broke out, Stripe broke out with them.

Stripe grew quietly but quickly. By the end of 2019, it was processing hundreds of billions of dollars a year for millions of businesses world-wide, and it counted heavyweights including

Amazon.com Inc.

among its customers.

In February 2020, with Covid-19 emerging, Stripe’s payment volumes out of Japan started to sag. At the end of the month, Stripe encouraged U.S. workers to stay home.

Chief Executive

Patrick Collison

decamped to his home on the coastline of California’s Sonoma County. Away from his brother for the longest stretch of their adult lives, he divided his time between Stripe and Fast Grants, a program to fund coronavirus research.

Across the payments industry, warning lights were flashing. As the economy shut down, stock prices slumped for competitors including PayPal and

Square Inc.

Stripe announced it had $2 billion in cash on its balance sheet, hoping to pre-empt any questions about its durability.

“We wanted to send a very clear message that they could rely on Stripe and Stripe wasn’t going anywhere,” said President John Collison.

Many of Stripe’s customers were suffering, especially travel businesses, whose own customers were demanding refunds on trips for which they already paid. That put Stripe in a bind: If a vacation planner went bust, the payment processor could be on the hook for making that business’s customers whole.

To protect itself, Stripe made many customers in the travel industry wait extra time to access their money, fueling resentment among small businesses already in a cash crunch. Other processors, including PayPal and Square, did the same.

For years, Stripe processed payments for David and Julie Nielsen’s family business that rented out five vacation homes on Cape Cod. People started canceling their stays in March and April 2020, forcing the Nielsens to tap their home equity to stay afloat. Then Stripe informed them there would be a two-week delay before it would release money deposited in their accounts, citing “an increase in customer refunds and chargebacks in your industry.”

“I was infuriated,” said Mr. Nielsen, who said Stripe never had to deal with a refund or chargeback related to his business. “There’s no partnership. They control all the power in that relationship.”

The Nielsens ended up having their best year ever in 2020. But Mr. Nielsen has been encouraging guests to pay with paper checks or apps such as Venmo in what he calls a “revenge tactic” against Stripe.

Still, new customers were joining all the time. Sectors such as telemedicine took off. An Irish sausage maker named Jane Russell’s signed up to sell directly to individuals after restaurants shut down. You Probably Need a Haircut, a website where out-of-work barbers gave online tutorials on DIY trims, went viral.

Greg Isenberg,

founder of You Probably Need a Haircut, said choosing Stripe was a no-brainer because it made accepting credit cards so effortless. “It’s like do you want your car to be automatic or manual? Sometimes it’s just nice that the gears shift themselves,” Mr. Isenberg said.

A survey of small-business customers of Stripe by Stanford University economists and Stripe’s top data scientist found that the average business suffered a slowdown for much of last year. But the top 5% increased their sales by 50% or more and expected those gains to endure.

“We could take a battering in the high seas and there was never any risk of the boat capsizing,” said

Michael Moritz,

a partner at venture-capital firm Sequoia Capital who invested early in Stripe and sits on its board of directors. “It was really just a question of how much deck damage there’d be.”

New and existing internet businesses favored Stripe for the investments it made in artificial intelligence and machine-learning models to help them increase their sales. Food-delivery company Postmates, for example, earned an additional $60 million last year after Stripe automatically updated the credentials on more than two million cards Postmates users had on file but which had recently expired.

Now, Stripe is laying the groundwork for an initial public offering it could pursue in late 2021 or early 2022, according to people familiar with the matter.

Ms. Suryadevara, the finance chief, declined to comment on whether Stripe is planning an IPO. She has been tasked with improving Stripe’s internal financial infrastructure, an effort code-named Project River, by the fourth quarter, according to people familiar with the matter. Stripe operates in 44 countries and multiple currencies, and reconciling the data is complicated.

Excluding what it pays other financial partners to facilitate payments, Stripe generated $1.6 billion in 2020 revenue, according to the people familiar with the company’s finances.

As it has gotten bigger, Stripe has been more in the spotlight. In January, it stepped into the political fray when it joined other tech companies in cutting off accounts tied to then-President

Trump

after the Capitol Hill riot.

Stripe also is pouring resources into its ambition to go beyond payments.

Last year, Stripe’s lending arm announced it would make small-business loans to customers of its customers, such as retailers that use

Lightspeed POS Inc.’s

software. An effort to offer bank accounts, debit cards and cash-management services to customers of

Shopify Inc.

and other platforms it serves is set to make its debut this year.

Whether current customers will want the new products is unclear. Ms. Suryadevara said the top 40 platforms that use Stripe for payment processing also use additional Stripe services. The company declined to provide figures on loan volume or nonpayments revenue.

Write to Peter Rudegeair at Peter.Rudegeair@wsj.com