Both Google (GOOG) and Facebook just sent out an internal memo about the move this morning.

UPDATE: Facebook, as well as Google, just confirmed that Fischer (pictured here) is joining the company.

Said Facebook COO Sheryl Sandberg:

“It’s a testament to Facebook’s expanding opportunities in advertising that we’re able to welcome an executive of David’s caliber. I have worked closely with David over the years and witnessed his passion, energy, and effectiveness at building teams on a global scale. David’s arrival deepens our operational capabilities so we can build upon our ability to serve advertisers, regardless of size or location, that are building their brands on Facebook.”

Said Google in a short statement: “We thank David for his many contributions to Google and wish him the best of luck in the future.”

But the search giant cannot be happy, as the move by Fischer is yet another in a series of top execs at the search giant to defect to the fast-growing social networking site.

And it will surely raise tensions between Google and Facebook, which are increasingly becoming rivals in several major Internet arenas, and opposing poles of power in Silicon Valley.

Fischer has a strong and longtime business relationship with Sandberg.

He was Sandberg’s top deputy when she ran the core self-serve ad business at Google and took over her job when she left for Facebook two years ago. The pair also worked together at the Treasury Department in Washington, D.C., in the Clinton administration.

It is clear that Fischer, said sources with knowledge of the situation, is being brought in to strengthen leadership in ad ops and help scale that business.

The appointment of the experienced exec also frees Sandberg and others to focus on nonadvertising issues, such as Facebook’s inevitable journey to an IPO in 2011 or 2012.

The affable Fischer, 37, has been at Google since 2002 and rose through its ranks quickly.

Said the Google Web site about Fischer, in part:

David Fischer is responsible for Google’s online sales channel, which represents the majority of the company’s customers worldwide. David has provided leadership for the online sales and operations program since its inception in early 2002 and has helped build Google’s online advertising network into the largest in the world. He also runs the online sales channel of the AdSense publisher program, which enables website owners worldwide to earn revenue through partnerships with Google.

David manages operations for Google’s consumer products worldwide and runs Google’s Book Search scanning operations, working with libraries and publishers around the world to digitally scan books from their collections. In addition, he leads the Google Grants program, which has donated more than $300 million advertising dollars to thousands of nonprofits around the world. David has opened many offices for Google, including its sales centers in Hyderabad and Gurgaon, India as well as Ann Arbor, Michigan and Boston, Massachusetts.

But Fischer left that job last fall, taking a sabbatical.

He returned to Google in January and has been working on the company’s efforts to expand its local advertising and commerce business.

In a statement, Fischer said of his new job:

“Facebook is not just driving a shift in how people connect with one another, but in how advertisers engage and interact with their customers. I’m eager to help accelerate this shift by working with customers, scaling operations globally, and collaborating with the product and engineering teams to continue to evolve Facebook’s advertising business. Google is an incredible company and I will miss the many friends I made during my time with the company. Facebook has assembled a highly impressive collection of talent, and I’m thrilled to be part of the team.”

At Facebook, Fischer will not lack for former Google execs to reminisce with.

As well as Sandberg, some of the many include: Elliot Schrage, who is VP of Global Communications, Marketing and Public Policy; Grady Burnett, who heads its online and inside sales; Don Faul, director of global online operations; and Ethan Beard, director of the Facebook Developer Network.

Please see this disclosure related to me and Google.

This isn’t Twitter’s first house call on Barack Obama. In March, CEO Evan Williams made a pilgrimage along with other youngish business people for a well-publicized economic summit.

But Dorsey, who was Twitter’s CEO until a year ago, seems to be making this trip solo, as part of a Washington tour he’s conducting himself.

Other stops, apparently, have included pop-ins at the State Department (“One goal of mine is to get Secretary Clinton back on Twitter”), the Department of Energy (“to talk about how Twitter can help encourage people to conserve energy everyday”) and a visit to Senator Claire McCaskill’s office, where he got a guided tour.

If this is the kind of stuff that has you on the edge of your seat, you can follow along with Dorsey’s travelogue here.

Dorsey, by the way, has 538,514 followers. The Obama administration, via its @whitehouse account, has 65,363.

[Image via Mobileman]

But–as many readers have requested–they will all be available in their entirety in this column.

Here’s Part 1 of 4 of an interview I did with Facebook Founder and CEO Mark Zuckerberg and COO Sheryl Sandberg. (I will post one video part of the discussion with Zuckerberg and Sandberg every day this week, starting Monday and concluding Thursday.)

The social-networking site has had quite a year, as the hottest and most hyped of the Web 2.0 landscape. With fast growth and still-questionable monetization power, where Facebook is going will be a journey plenty will be paying attention to.

In this video, I get a Princess Phone from Zuckerberg and Sandberg and apologize to Zuckerberg about calling him “toddler CEO.” Then Zuckerberg talks about sharing information, learning to develop by hacking on AOL, and his time at Harvard University, and Sandberg talks about her time at Harvard, in the Clinton administration and at Google.