Vice President Joe Biden's son and a close friend of Secretary of State John Kerry's stepson have joined the board of a Ukrainian gas producer controlled by a former top security and energy official for deposed President Viktor Yanukovych.

The move has attracted attention given Messrs. Biden's and Kerry's public roles in diplomacy toward Ukraine, where the U.S. expressed support for pro-Western demonstrators who toppled Mr. Yanukovych's Kremlin-backed government in February. The uprising provoked a pro-Russia backlash that has plunged the post-Soviet republic into conflict and bought it to the brink of civil war.

Hunter Biden, a lawyer by training and the younger of the vice president's two sons, joined the board of directors of Ukrainian gas firm Burisma Holdings Ltd. this month and took on responsibility for the company's legal unit, according to a statement issued by the closely held gas producer.

His appointment came a few weeks afterDevon Archer—college roommate of the secretary of state's stepson, H.J. Heinz Co. ketchup heir Christopher Heinz—joined the board to help the gas firm attract U.S. investors, improve its corporate governance and expand its operations.

"The fact that I joined the board of directors is largely based on the company's will to grow," Mr. Archer said in an interview with Ukrainian media published on Burisma's website. "Last year alone witnessed a lot of transformations." He vowed to make the company more transparent.

Mr. Biden, 44 years old, and Mr. Archer, 39, work for Rosemont Seneca Partners, a U.S. investment company. It is affiliated with Rosemont Capital, a private-equity firm Mr. Archer co-founded with Mr. Heinz.

Two people familiar with Mr. Heinz's involvement in the firms said he isn't involved with the day-to-day operation of Rosemont Seneca, which is 50%-owned by Rosemont Capital. The people also said there was no financial investment by the firms in Burisma, just board memberships for Messrs. Biden and Archer.

Messages were left for Hunter Biden at his offices in Washington and New York and at offices of a law firm where he is of counsel. A person answering the phone at his office in Washington said Messrs. Biden and Archer were unavailable and promised to pass along a message.

The White House press secretary and the vice president's office described Hunter Biden's activities as those of a private citizen, bearing no endorsement of the U.S. government.

"Hunter Biden is a private citizen and a lawyer," said Kendra Barkoff, a spokeswoman for Joe Biden's office. "The vice president does not endorse any particular company and has no involvement with this company."

The board appointments come amid a broader push at Burisma to step up standards and investment. Alan Apter, an American investment banker who has worked in the former Soviet Union, joined Burisma as chairman of the board last year and received a mandate to improve the company's corporate governance and attract foreign capital. He said he met Mr. Archer, a longtime financier and entrepreneur, through mutual friends and invited him and later Mr. Biden to join the board.

"This is totally based on merit," Mr. Apter said. He said none of the independent directors holds a stake in the company. He said they would receive a salary for independent directorship commensurate with world-class experience but declined to name the sum.

Burisma is one of a handful of privately owned gas companies that together account for a little more than 10% of Ukraine's domestic production. The rest of the production comes from gas companies fully or partially owned by the Ukrainian state. Burisma's biggest subsidiary, Esko Pivnich, pumps gas from the Poltava region east of Kiev.

The gas producer is controlled by Nikolai Zlochevsky, a former member of Parliament for Mr. Yanukovych's Party of Regions, according to a person familiar with the matter. He served as Mr. Yanukovych's minister of environmental protection from July 2010 and then become minister of ecology and natural resources in December 2010, key positions with influence over the oil and gas industry.

Mr. Zlochevsky was removed from the post in April 2012 and appointed deputy secretary of Ukraine's National Security and Defense Council, a role he held until Mr. Yanukovych's government collapsed in late February. During his tenure as a government minister, Burisma and entities associated with the firm received a large number of permits for oil and gas exploration in Ukraine and stepped up their output considerably, according to Ukrainian press reports.

Mr. Zlochevsky couldn't be reached for comment.

Mr. Yanukovych, who was sanctioned by the U.S. in March, has taken refuge in Russia.

Burisma produced about 450 million cubic meters of gas in 2013 and became the largest independent gas producer in Ukraine by volume in the first quarter of this year, according to a company spokesman. The production figures couldn't be independently verified.

The Ukrainian company sells its gas domestically. It is poised to benefit from the rising gas prices the country is likely to see in the future, now that Russia has removed a discount on gas deliveries for Ukraine in response to what it sees as the rise of anti-Kremlin authorities in Kiev.

Ukrainian regulatory authorities cap gas prices for domestic industrial customers. The cap averaged about $425 per thousand cubic meters of gas last year. Though Burisma doesn't reveal financial figures, calculations suggest the company's production last year would have commanded more than $191 million in revenue on the domestic market at those rates.

Mr. Apter said Burisma's expansion could help reduce Ukraine's energy dependence and thereby help ease its political problems.

"The country is quite gas dependent and one would expect, like most countries, there is a desire to be independent of foreign sources, be they in Russia or elsewhere," Mr. Apter said. "It helps the country."

Burisma has now added deep U.S. political connections to its arsenal.

In addition to being Mr. Heinz's college roommate at Yale, Mr. Archer was an adviser to Mr. Kerry's presidential campaign in 2004 and co-chaired his National Finance Committee. According to his biography, he serves as a trustee of the Heinz Family Office, which manages the family business.

Hunter Biden's business activities have attracted attention before.

His work as a lobbyist when his father was in the U.S. Senate came under scrutiny. Shortly after his father became Barack Obama's running mate in 2008, he gave up his lobbying career and resigned his partnership at a Washington lobbying firm.

When he had been senator, Mr. Obama sought more than $3.4 million in earmarks for clients of Hunter Biden, and succeeded in getting $192,000 for St. Xavier University near Chicago, according to public disclosure records.

At the time, a spokesman for Mr. Obama said Hunter Biden hadn't met with the senator himself but rather with office staff. The spokesman also said it wasn't surprising to see Mr. Obama was fighting for interests and institutions in his home state of Illinois.

In early 2009, The Wall Street Journal reported that Hunter Biden and his uncle had run a fund of funds that was being marketed exclusively by Texas financier R. Allen Stanford's companies. Mr. Stanford later was sentenced to 110 years in prison for masterminding a $7 billion Ponzi scheme.

At the time of the Journal article, a lawyer for the Bidens said the fund terminated the relationship and offered to return $2.7 million in investment that companies controlled by Mr. Stanford had given the fund. He said the Bidens had never met Mr. Stanford.

—Colleen McCain Nelson contributed to this article.

Write to Paul Sonne atpaul.sonne@wsj.com