Whole Foods shareholders and federal regulators approved Amazon’s $13.7 billion acquisition of the organic grocer, a deal that could bring big changes to the supermarket industry and how people order groceries online.

By buying Whole Foods, Amazon is taking a bold step into bricks-and-mortar, with more than 460 stores and potentially very lucrative data about how shoppers behave offline.

Whole Foods shareholders gave their blessing to the acquisition that its CEO had called “love at first sight.” And the Federal Trade Commission said in a brief statement that it had looked into competition concerns and would not block the deal.

The FTC investigated whether the takeover “substantially lessened competition” or “constituted an unfair method of competition,” said Bruce Hoffman, the acting director of the agency’s Bureau of Competition. “Based on our investigation we have decided not to pursue this matter further.”

A union that represents food industry workers had asked the FTC to scrutinize the deal closely, saying it could hurt competition and lead to job cuts. Regulators tend to block deals when two direct competitors are combining, and Amazon — despite its dominance in the online marketplace — doesn’t currently have a big groceries business.

Before the deal was announced in June, Whole Foods had been under intense shareholder pressure to improve results and retain customers who have more choices about where to get natural foods. As Whole Foods grew, more supermarkets offered similar organic and natural foods, but at cheaper prices.

As part of the deal, Amazon will pay Whole Foods shareholders $42 for each share they own. That was an 18 percent premium from its stock price the day before the tie-up was announced on June 16. Shares of Whole Foods Market, which is based in Austin, Texas, ended Wednesday at $41.68.

Earlier this month, Amazon sold $16 billion of bonds in order to pay for Whole Foods. Seattle-based Amazon has said it expects the deal to close before the end of the year.