Robinhood Markets Inc. named three new directors to its board on Tuesday, as the stock-trading startup laid more of the groundwork for what is expected to be one of the year’s most eagerly awaited initial public offerings.

The new Robinhood board members are former Apple Inc. and Bridgewater Associates executive Jon Rubinstein, PricewaterhouseCoopers LLP partner Paula Loop and former World Bank President Robert Zoellick. Messrs. Rubinstein and Zoellick’s appointments are effective immediately, and Ms. Loop’s will be effective June 17.

With its easy-to-use smartphone app and commission-free business model, Robinhood skyrocketed in popularity this year amid market rallies in meme stocks like GameStop Corp. and cryptocurrencies like dogecoin. Robinhood’s financial performance boomed in the first quarter, with its biggest revenue source more than tripling. The company confidentially filed paperwork with the Securities and Exchange Commission in March with an eye toward listing its shares publicly as early as June, The Wall Street Journal previously reported.

But Robinhood’s operations and corporate governance didn’t scale at the same rate as its user base, forcing the company to grow up in a hurry. For instance, it struggled this year to deal with a thicket of customer help requests, many related to its surprise decision in January to restrict trading in some highflying stocks. Robinhood has pledged to more than double the number of customer-support agents on staff this year.

Until Tuesday’s appointments, Robinhood’s board looked more like that of a startup than a multibillion-dollar, soon-to-be-public company. Co-founders Vlad Tenev and Baiju Bhatt held two of the four seats, and the other two were held by Robinhood’s venture-capital backers. The Menlo Park-based company didn’t have a female director, which would have put it at odds with a 2018 California law requiring all publicly traded companies with headquarters in the state to have women on their boards.

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The new directors are old hands when it comes to public-company board experience. Mr. Rubinstein is on the board at Amazon.com Inc., and Mr. Zoellick is on the board of Twitter Inc.

Robinhood’s IPO preparations also involve rolling out a new system that allows users to access new listings, including its own, on terms similar to bigger investors. Last month, the company debuted that platform when medical-apparel startup Figs Inc. said it would allocate up to 1% of its IPO to individual investors on Robinhood.

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

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