SAN FRANCISCO — Uber’s board of directors voted on Tuesday for governance changes that reshape the balance of power at the ride-hailing company and that pave the way for a stock sale to the Japanese conglomerate SoftBank.

The 11-member board approved some of the terms from a proposal put forward last week by Dara Khosrowshahi, Uber’s new chief executive, and Goldman Sachs, the investment bank that is an investor in the privately held company.

Under the terms agreed to on Tuesday, the clout of certain Uber shareholders — including, most significantly, its former chief executive, Travis Kalanick, who is a board member — will be reduced. Other measures that had been in consideration, including one that would have posed hurdles to Mr. Kalanick’s returning as chief executive, were dropped from the proposal before the meeting.

Still, the board approved enough changes for Uber to move forward on an investment from SoftBank. SoftBank has held discussions to buy a significant chunk of Uber’s stock, but the deal was contingent on changing the company’s governance structure so that some of its early investors would have an incentive to sell.

In a statement, Uber’s board said it had “voted unanimously to move forward with the proposed investment by SoftBank and with governance changes that would strengthen its independence and ensure equality among all shareholders.”

The board’s decisions mean that Uber, valued at nearly $70 billion and closely watched by other start-ups, may have defused — at least temporarily — another fractious situation. Board members have been deeply split for months on many issues, with Uber grappling with numerous scandals over its workplace culture and management.

The board’s recent divisions have been rooted in a fractured relationship between Mr. Kalanick and Benchmark, a venture-capital firm that was an early investor in Uber and that holds a board seat. Benchmark helped force out Mr. Kalanick as chief executive in June.

Since then, Benchmark and Mr. Kalanick have warred over how much control of Uber he retains. Mr. Kalanick had outsize voting rights at the company under a certain class of Uber stock that he owns, and he controls three board seats under an amendment to the corporate charter that was passed last year.

On Tuesday, Uber’s board agreed to remove the special voting power carried by two categories of Uber stock, the class B common shares and the preferred shares. Mr. Kalanick holds about a third of Uber’s class B common stock, which originally came with 10-to-one voting power. The preferred stock, which also had special voting rights, is held by early venture investors in Uber including Benchmark.

All of Uber’s shareholders will eventually have one vote per share, regardless of the class of company stock that they own.

At the time they were proposed, the corporate governance changes put forth by Mr. Khosrowshahi were supported by many board members, according to two people briefed on the conversations among board members. But Mr. Kalanick spent the past week pushing back on some of the details. To gain more leverage on the board, he appointed two additional board members, Ursula Burns, a former chief executive of Xerox, and John Thain, a former chief executive of Merrill Lynch, last week.