In general, the code compels tech companies and news publishers to submit to binding arbitration if they can’t reach a deal on payment. The amendments announced Tuesday include requiring an additional round of negotiation before binding arbitration kicks in, as well as more acknowledgment of any deals Facebook reaches with publishers on its own.

Alphabet Inc.’s

GOOG 0.29%

Google also initially opposed the legislation, at one time threatening to shut down its search engine in Australia. Recently, though, it opted instead to sign content deals with a number of publishers—including

News Corp,

which owns big newspapers in Australia as well as Dow Jones & Co., the publisher of The Wall Street Journal.

News Corp has supported the law.

Parliament’s upper chamber, the Senate, passed the legislation with the Facebook amendments late Wednesday. It will now return to the lower chamber, the House of Representatives—which earlier passed the unamended version—for a vote as early as Thursday. Prime Minister

Scott Morrison’s

center-right government effectively controls the lower chamber.

The code will become law when it is signed by Australia’s governor-general, the representative of Britain’s Queen Elizabeth II, Australia’s head of state.

Australia’s effort to compel the tech companies to pay for news has been watched globally, and there are signs of momentum for similar legislation in other countries. In Canada, for example, one minister has said his government intends to introduce measures. Canadian Prime Minister

Justin Trudeau

recently spoke with Mr. Morrison about potential regulatory cooperation.

Both Google and Facebook have previously paid for news in some cases. News Corp already has a commercial agreement to supply news through Facebook. Google has signed deals with more than 500 publications in a dozen countries, including Germany, the U.K. and Australia, for a product called News Showcase, and it has pledged $1 billion over three years to such licensing deals.

Australian officials have previously said that the code’s purpose is to encourage the tech companies and media outlets to strike deals on their own, after media companies complained that the digital platforms’ market power meant they had no incentive to negotiate.

The tech giants have argued that when their platforms send users to news websites, publishers benefit. Other business groups and some computer scientists have also raised concerns about the law.

Write to Mike Cherney at mike.cherney@wsj.com