Starting in 2022, BlackRock says its large investors can vote themselves on everything from who sits on boards to executive pay to what companies should disclose on greenhouse gas emissions. The change allows those BlackRock clients to lay claim to voting power on some $2 trillion in investments tied to index-tracking assets BlackRock manages in institutional accounts. This is about 40% of roughly $4.8 trillion of indexed equities managed by BlackRock.

“We believe clients should, where possible, have more choices as to how they participate in voting their index holdings,” BlackRock said in a client note on Thursday announcing the changes.

BlackRock and other large asset managers have faced criticism over their vast voting power. The Securities and Exchange Commission proposed a rule last month that would require money managers to disclose more information on how they vote on behalf of their clients.

The $9.5 trillion firm rose on the back of a yearslong stock rally and indexing boom to become a top three shareholder of more than 80% of the companies in the S&P 500 through its funds, according to S&P Global Market Intelligence from earlier this year. In the past year, BlackRock funds cast key votes that helped shake up

Toshiba Corp.’s

board, and elect new board members at oil major

Exxon Mobil Corp.

, among the thousands of votes cast by BlackRock funds.

BlackRock has said the team overseeing voting follows strict guidelines to maximize investor returns.

As part of the changes, BlackRock will let large investors pick and choose resolutions on which they want to vote. An investor could decide to just vote on oil-and-gas companies or private prisons or gun makers—or all companies. The investor can vote in line with their own rules or values, or vote with firms such as proxy adviser Institutional Shareholder Services.

This is the culmination of a yearslong effort by BlackRock to build the technology infrastructure to direct proxies to clients, sync up various parts of the shareholder voting ecosystem and make sure investors can deliver ballots on time.

In the past, certain BlackRock clients have voted their own proxies on some $480 billion in indexed assets managed by the firm, but BlackRock didn’t have systems to accommodate more.

If the organizations eligible for this choice exercise their full voting power, this would lead to a transfer of votes on some $1.5 trillion in assets from the hands of BlackRock to clients.

BlackRock said that it is “committed to exploring all options to expand proxy voting choice to even more investors.” That includes individual investors in exchange-traded funds and index mutual funds.

Over the years, academics and politicians have questioned whether BlackRock has too much influence through its votes.

In 2018, in response to the index fund boom, Harvard Law School professor

John Coates

warned that voting power would be controlled by a small group of people with “practical power over the majority of U.S. public companies.”

BlackRock and other index giants have started to use their votes more aggressively. Environmentalists and activists have frequently called on the biggest asset managers to do more to penalize oil companies, while some investors worry about overreach in their votes.

The world’s second-largest asset manager, Vanguard Group, handed off some of its voting power in 2019, so outside managers running the firm’s active stock funds vote separately from funds it manages on its own.

In its client note Thursday, BlackRock said: “This initiative is consistent with wanting to offer clients choice across everything we do—the money we manage is not our own, it belongs to our clients.”

Write to Dawn Lim at dawn.lim@wsj.com