Friendly governments that are themselves lenders to Ukraine, including the U.S., U.K., France and Germany, had supported the payment delay, and urged bondholders to approve the requests. Ukraine’s Finance Ministry also said it received indications of support from major holders of its bonds, including BlackRock Inc., Fidelity Investments, Amia Capital LLP and other investors.

Results of the vote released Wednesday showed the holders of about 75% of the outstanding bonds agreed. Investors in Ukraine’s securities linked to its gross domestic product also approved changes to the coupon payments of those assets.

“There’s a very clear rationale for passing this,” said Daniel Wood, a portfolio manager at William Blair Investment Management, who voted in favor of delayed payments on Ukraine bonds he holds. Mr. Wood said the situation was unique, adding: “Why would you divert that [money] to bondholders when the money is needed elsewhere at the moment?”

The approval of the deferrals is expected to save Ukraine’s government up to $6 billion in payments on its sovereign debt, according to Timothy Ash, a strategist at BlueBay Asset Management.

The move will also help Ukraine to avoid defaulting on its obligations due to a growing cash shortfall. Kyiv narrowly avoided default in 2015, instead reaching a debt-relief deal with its creditors. Private creditors agreed to a 20% write-down in the face value of their Ukrainian bonds, and to push back maturities on government debt by four years. The GDP-linked securities were issued then as a sweetener for creditors.

Some investors only submitted last-minute approvals, leaving the outcome uncertain until roughly an hour before the voting deadline, according to people familiar with the matter. Creditors holding nearly half of a $912 million bond due later this year didn’t give indication that they approved until late Tuesday afternoon, the people added.

If those creditors hadn’t signed off, Ukraine would have had to pay the bond in full when it matured or risk defaulting on its debts.

To secure approval for changes to its GDP-linked securities, Ukraine agreed to pay holders a consent fee. In exchange, investors agreed to halve the maximum payment they will receive in 2025: to 0.5% of Ukraine’s GDP from 1%. The government also secured options allowing it to redeem the securities starting in 2024.

Without a restructuring, the GDP securities could have become a major financial burden. These entitle investors to receive payments equivalent to a portion of Ukraine’s growth in GDP when it exceeds 3%. Ukraine’s economy is likely to boom if it eventually succeeds in repelling the Russian invasion, as aid potentially totaling hundreds of billions of dollars flows into the country for reconstruction.

The changes reduce the risk that Ukraine will have to pay a large part of its postwar economic recovery to financial investors.

However, Ukraine’s finances remain under extreme pressure. The Finance Ministry in Kyiv has estimated its financing shortfall stands at roughly $5 billion a month, with tax revenue only covering 30% to 40% of its spending needs, which include heavy military expenditures.

Ukraine has foreign-exchange reserves of just over $22 billion, according to central-bank data, down from $31 billion at the beginning of the year.

Kyiv on Friday formally requested additional fiscal assistance from the International Monetary Fund, which provided a $1.4 billion loan to the government in March. The U.S. and Europe have now pledged some $25 billion in financial assistance, but only $6 billion in loans and grants have been disbursed to Ukraine as of early August, government figures show.

State-owned Ukrainian companies have also announced their intention to delay payments as the war nears its sixth month.

—Matt Wirz and Chelsey Dulaney contributed to this article.

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com and Alexander Saeedy at alexander.saeedy@wsj.com