So has a company that bills itself as the anti-Groupon (GRPN) found a formula that works for both consumers and retailers? That’s the hope of Hjalmar Winbladh, a serial entrepreneur whose Swedish startup, Wrapp, is launching in the United States on Monday. “From a retailer perspective, we can send the right customer to your store and help drive more sales,” says Winbladh, who is Wrapp’s CEO.

Wrapp is not daily deals startup — there are already hundreds of those, none of them runaway successes. Wrapp is a social gifting mobile app, whose name is a mash-up of “wrap” and “app,” and is built atop of Facebook’s social graph. It encourages users to give gifts to their friends and relatives on birthdays, holidays and other special occasions. But instead of giving, say, a virtual martini, Wrapp users give each other virtual gift cards that are redeemable, via their mobile phones, at major retailers like Gap (GPS), H&M or Sephora.

Many of the cards are free and retailers can specify to whom they are available (women 18 to 24 in Chicago, for example). If you are the one doing the giving, you can add money to a card. You can also publish your gift on Facebook, where others can also add money to it. (“Hey, Joe is running a half-marathon, so lets all contribute to a his new pair of running shoes.”) Since the mobile app has access to Facebook data, it will remind you of your friend’s birthdays and other special occasions.

“Wrapp will be a fantastic way to give a gift,” says Bridget Dolan, vice president of interactive at Sephora. Dolan says many people who have the intention to give gifts often don’t do so because they don’t have time or because they forget. “With Wrapp, you are going to act on those intentions because it is so easy. It is the perfect ‘oops’ gift.”

Sephora already works with eGift Social, which lets people send gift cards via Facebook, but Dolan says Wrapp’s mobile app and its ability to remind users about special occasions has the potential to put Sephora’s gift card business on a “very fast viral climb.”

Like Groupon, Wrapp will drive online denizens to brick-and-mortar stores, says Winbladh. However consumers won’t associate the shopping experience with a discount, which can tarnish a brand’s cachet, but rather with a gift purposely chosen by their friends, he says. And brands will get free advertising, of sorts, when Wrapp users publish their gifts, join as a group to make a gift bigger, or “like” their friend’s gifts on Facebook.

Even Groupon investor and startup sage Reid Hoffman suggests that Wrapp could prove more effective for retailers than daily deals. “It has a similar value proposition but appeals to consumers in a very different way,” says Hoffman, who invested in Wrapp’s $10.5 million Series A round in January and joined the company’s board of directors. “It’s not saying, ‘hey, my product is worth less than I charge for.’ It’s a different kind of marketing promotion.”

Hoffman was joined on Wrapp’s board by fellow high profile investor, Niklas Zennström, the cofounder of Skype (MSFT) and Kazaa, through his London-based venture capital firm, Atomico.

Wrapp is opening in the United States with 10 brands, and Winbladh says another 15 merchants will join in a matter of weeks. The company makes money by charging retailers a transaction fee and a percentage of paid cards that are gifted through the app.

Wrapp launched in Sweden in November, and more recently opened its service in the U.K. and Norway. Since then, it has amassed about 165,000 active users that have gifted more than 1.4 million cards. On average, retailers saw a lift in sales that was more than four times the value of the free cards.

Given the size and growth of the U.S. gift card market — more than $30 billion in cards were given during the 2011 holiday season alone — it’s not hard to see why Winbladh, Hoffman and Zennström are salivating at the prospect of Wrapp’s U.S. launch. Says Winblath, “We are 100% aligned with the retailer.”