Toshiba shares rose after the announcement and closed 1.6% higher in Tokyo trading.

In November, Toshiba had said it planned to split into three units, one focusing on infrastructure, a second on electronic devices and a third to manage the company’s stake in flash-memory company Kioxia Holdings Corp. and other assets.

Some shareholders publicly expressed dissatisfaction with that plan, calling for stronger measures to lift the value of the long-struggling technology conglomerate. Objecting shareholders have also said they want to make it easier to block any plan they find inadequate.

In an open letter sent in early January, a major Toshiba shareholder, Singapore-based 3D Investment Partners Pte., called the plan “the result of a flawed process” that failed to address the company’s underlying issues.

It asked Toshiba’s strategic-review committee to consider alternatives, including selling the whole company to a private investor.

Another shareholder, Farallon Capital Management LLC, said Toshiba should seek approval of two-thirds of its shareholders, rather than a simple majority, to go ahead with its separation plan.

“The core issue afflicting Toshiba is the lack of trust between management and its shareholders, resulting in four years of prolonged conflict,” the U.S. investment firm said Jan. 18. “The very need for a shareholder to raise such a self-evident point even after the repeated governance failures only exacerbates the situation.”

Paul Brough, a Toshiba independent director who heads its strategic-review committee, said Monday the two-way-split plan reflected shareholder input. He said the board was focused on increasing shareholder returns and selling noncore businesses.

Earlier Monday, Toshiba said it would sell a 55% stake in an air-conditioner joint venture to its partner, Carrier Global Corp., for about $868 million. The company also said it planned to sell its elevator and lighting businesses.

Toshiba has gone through repeated upheavals since an accounting scandal emerged in 2015, and foreign shareholders now hold big stakes.

Tensions between the company and shareholders grew after a report released in June 2021 found evidence of broad collaboration between the company and government officials to stifle foreign shareholders’ voices ahead of an annual shareholder meeting in July 2020. One executive wrote an email saying that the group’s way of dealing with those shareholders was to “beat them up,” according to the report.

Write to Megumi Fujikawa at megumi.fujikawa@wsj.com