MOUNTAIN VIEW — Google’s (GOOG) same-day delivery service will make its public debut to most of the Bay Area on Wednesday morning, as the search engine giant becomes the latest tech company to deliver online purchases to customers’ homes just hours after they click the purchase button.

The public launch makes Google’s once-exclusive service available to everyone who wants same-day delivery from San Francisco to San Jose, and signals that the Internet company may have found the formula to solve one of the most challenging problems in retail. Shopping Express is a Web and mobile site — which goes live online at 7 a.m. — where customers can shop from more than 15 Bay Area retailers including Walgreens, Nob Hill Foods, Staples, Blue Bottle Coffee, Target and Palo Alto Sport Shop and Toy World, and Google will deliver the purchases that day within a three- to five-hour window. The cost is $5 for each store pickup.

“This new service brings the speed of the Web to the real world by helping you shop your favorite local stores online — in a single place — and get what you need delivered the same day,” Tom Fallows, who heads up Google Shopping Express, wrote in a company blog.

With this week’s launch, Google wraps up more than six months of testing on Shopping Express, which was spent revising algorithms and delivery routes, and crunching data to predict product departure and arrival times. The service started last year as an experiment with Google employees, and in March launched as an invitation-only service to a select group of people who applied. Google struggled with some of the logistics in its early testing, and was forced to cancel some deliveries after making mistakes with store inventory, Fallows said in an interview in August with this newspaper.

“This has been a long time coming,” he added Tuesday.

Google on Wednesday will also announce the Shopping Express applications for Android and iOS smartphones, which can be downloaded from the Google Play Store and the Apple (AAPL) App Store. And the company added a few more retailers to the mix — including Guitar Center, REI and Whole Foods, for any shoppers who want hiking boots and quinoa delivered to their front door.

The East Bay isn’t yet covered by the delivery service: “We want to bring in as many people as possible,” but the company is starting with San Francisco and the Peninsula, Fallows said.

Google joins eBay (EBAY) and Amazon in the race to win the local commerce market by connecting consumers with neighborhood retailers for everyday shopping needs. Nationally, this is a $2 trillion-a-year market, which includes cleaning products, groceries and health and beauty items, according to J.P. Morgan estimates. Same-day delivery also opens the door to selling advertising and other technology to retailers, and building a loyal following of consumers who see Google Shopping Express as their one-stop daily shopping destination.

Contact Heather Somerville at 510-208-6413. Follow her at Twitter.com/heathersomervil.