Many companies doing business in the European Union could face big changes as the EU moves ahead with an effort to keep multinationals like Apple Inc. from taking advantage of discrepancies in tax codes across the 28-nation bloc.

The European Commission, the EU’s executive arm, published a proposal last week for a uniform set of rules on taxing corporate profits. The initiative—known as the common consolidated corporate-tax base, or CCCTB—would require multinational companies to pay taxes based on where their assets and employees are located and where their sales take place.

The commission and other European institutions are hoping to curb what they regard as creative tax reporting, tax dodging and sweetheart deals that some EU countries use to attract big employers.

In August, for example, the commission ordered Ireland to collect roughly €13 billion ($14.2 billion) in allegedly unpaid taxes from Apple, calling arrangements that its government offered Apple in 1991 and 2007 “illegal tax benefits.”

Apple declined to comment.

Corporate finance executives already are gearing up for the challenge and anticipate a lot of work to comply with the new European rules, which could take years to be fully implemented.

“This will have a significant impact on our corporate-tax reports, and I want to be able to give a rough estimate during the next 12 months on the potential impact on our business,” said Werner Stuffer, head of tax at ZF Friedrichshafen AG, a large German automotive supplier. ZF does business in most EU countries, and often has multiple subsidiaries in those countries, which require it to make an average three to five tax declarations per nation.

Under the new rules, Mr. Stuffer would no longer have to navigate different national methods of calculating equity, debt and other items on his balance sheet. “This would smoothen the process of reporting our taxes,“ he said.

To become law, the CCCTB would need unanimous approval by all 28 EU member states and subsequent approval by each of their national parliaments.

If enacted, the law would take effect in two phases. In the first, companies whose European operations have more than €750 million, a year in revenue would have to calculate their taxable profits under a set of accounting rules that apply across all EU countries. The rules wouldn’t prevent EU member states from setting their own corporate-tax rates.

Later, after the new tax code fully kicks in, companies would have to pay taxes in member states based on three criteria: assets, employees and sales.

The EU says the CCCTB would eliminate 70% of profit-shifting—the maneuvering many companies do to transfer their income and expenses between branches to reduce their overall tax liabilities. Experts say companies will have to run simulations in order to tell how much the tax changes will influence their financial position.

Although ZF expects its overall corporate-tax obligations to remain unchanged, its tax contributions could go down once the second part of the CCCTB took effect, Mr. Stuffer said. “I expect our tax revenue in Germany to go down whilst it will go up in our more capital-intensive markets in Eastern Europe,” he said.

According to KPMG International’s tax table, the corporate-tax rate stands at 29.72% in Germany, 19% in Poland, Hungary and the Czech Republic and 22% in Slovakia. ZF operates in all five countries.

The EU’s Council of Ministers, its top decision-making body, aims to discuss the first part of the proposed rules in 2017. It plans to discuss the second phase only after it agrees on the first part.

“There is a lot of work involved in implementing CCCTB,” said Nicholas Aleksander, a tax partner at Gibson, Dunn & Crutcher LLP in London. “Each and every company will have to develop a view on how this affects them.”

“For internet companies without a lot of physical assets on the ground, this will bring profound changes,” said Mr. Aleksander. Those companies might be forced to pay a larger part of their taxes in the country where they have the most assets, the most employees and the highest sales.

EBay Inc., the big e-commerce company, is among those that could be affected. It paid £1.1 million ($1.3 million) in corporation tax in the U.K. in 2015, according to filings with Companies House, the U.K.’s companies registrar. That was a pittance beside the $1.4 billion in revenue the company said it got from the U.K., its second-largest market.

“In all countries and at all times, eBay is fully compliant with national, EU and international tax rules,” an eBay spokesman said.

SAP SE lauded the commission’s intention to “introduce Europe-wide tax incentives for research and development,” a company spokesman said. But the German software maker warned that “double taxation is still a reality for many companies” in Europe, and needs to be eliminated “at least within the EU.”

Mr. Aleksander said it isn’t clear whether CCCTB would discourage U.S. companies from tax inversions. In a tax inversion, a company shifts its tax residence to a lower-tax country—often in Europe—sometimes by acquiring a company based there.

“It is going to depend on whether CCCTB eventually leads to higher corporate taxes in Europe, which would in turn reduce the attractiveness of an inversion,” he said.

Write to Nina Trentmann at Nina.Trentmann@wsj.com