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 brought 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 after Devon 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. A State Department spokesman declined to comment.

"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.