Amazon announced on Thursday that its $13.7 billion acquisition of Whole Foods will close on Monday.

As the two companies work to integrate their business, all customers will immediately see "lower prices on a selection of best-selling staples across [Whole Foods] stores."

And Amazon promises "more to come," as the internet giant begins to integrate Prime into the Whole Foods ecosystem. Eventually, Prime members will receive "special savings and in-store benefits."

Amazon didn't disclose how long that would take, but said it would first need to integrate Amazon Prime into the Whole Foods point-of-sale system. Once complete, the offers will begin and eventually Prime will become Whole Foods' customer rewards program.

Grocery stocks immediately tumbled Thursday afternoon on the news. Shares of Kroger, Costco, Sprouts Farmers and Supervalu were all seen trading at session lows. Big-box retailers Target and Wal-Mart also watched their stocks fall.

Amazon promising immediate price cuts puts pressure on traditional grocers that are already operating in a thin-margin business. Meal-kit businesses, like Blue Apron, have also taken a beating after Amazon announced it would be creating a similar service.

On Wednesday, Whole Foods shareholders voted to advance Amazon's acquisition of the grocery chain, moving the proposal one step closer to reality. Amazon shareholders didn't need to sign off on the deal.

The two parties were saying they expected to finalize their merger during the second half of 2017. Though, a source familiar with the matter told CNBC the deal could happen "sooner rather than later."

Just hours after Wednesday's shareholders vote, the Federal Trade Commission said it would allow the Amazon-Whole Foods deal to proceed. The FTC had been conducting an investigation to gauge whether the merger would decrease competition under federal regulations.

A spokesperson from Amazon told CNBC on Thursday that it has no plans for layoffs or to use automation to replace Whole Foods' cashiers. This was a widely held concern that sparked debate when the acquisition was first announced.

Looking at the future of Whole Foods stores, Amazon said that soon Amazon Lockers will be available in select locations. Using these, shoppers can either have products shipped from Amazon.com to their local Whole Foods, or return items back to Amazon during a trip to the grocer.

Whole Foods' private-label products will also now be available through Amazon.com, AmazonFresh, Prime Pantry and Prime Now. A move like this could put more pressure on competitors on the low-price end of the supermarket spectrum, like Wal-Mart, and German-based Aldi and Lidl.

And this is particularly concerning for those companies, like Sprouts, that operate neck and neck with Whole Foods in organic. Here, prices have tended to be higher than with conventional and nonperishable items.

"The bottom line is that this isn't theory any more," GlobalData Retail Managing Director Neil Saunders told CNBC. "The deal is happening and it will drive change in the grocery sector. Competitors will need to think about what that means for them and respond accordingly."

Among many things, this deal will provide Amazon a much more extensive real estate footprint. However, Amazon is entering the brick-and-mortar world at a time when many are saying the supermarket space is overcrowded.

Some of the bigger names in grocery are already trimming plans for expansion. Kroger, for example, has said it will cut its store openings in 2017 to 55 from 100, opting to invest less in its physical retail and more in digital initiatives. Even Whole Foods had scaled back its own expansion plans prior to Amazon arriving on the scene.

In its press release on Thursday, Amazon didn't mention exactly how it would use Whole Foods' portfolio of more than 450 stores — whether it would keep all locations open, or transform them over time.