Levinson, the former chairman and CEO of Genentech (DNA), joined Apple’s board in 2000 and Google’s in 2004.

Since then, the two companies have become increasingly competitive, and last May the FTC began an inquiry into whether the presence of Levinson and Google CEO Eric Schmidt on both boards violated the interlocking directorates provision of the Clayton Antitrust Act.

Schmidt resigned from Apple’s board in July. Google announced on Monday that Levinson was resigning from its board, effective immediately.

No reason was given, although Schmidt did issue a statement:

“Art has been a key part of Google’s success these past five years, offering unvarnished advice and vital counsel on every big issue and opportunity Google has faced,” it read. “Though he leaves as a member of our Board, Art will always have a special place at Google.”

Two weeks ago, Schmidt denied that he had resigned Apple’s board under pressure and said there was no reason for Levinson to leave Google’s. “I would hope not,” he told reporters when asked whether Levinson would be stepping down, “because I don’t think it’s necessary.” (link)

It remains to be seen whether the FTC will now call off its inquiry. The only remaining overlaps are Al Gore and William Campbell, who are both Apple board members and senior advisers to Google. Campbell actually sits in on Google’s board meetings, the only outsider who does so.

But a statement issued by FTC chairman Jon Leibowitz seemed to suggest that the commission considers the case closed.

“Google, Apple, and Mr. Levinson should be commended for recognizing that overlapping board members between competing companies raise serious antitrust issues and for their willingness to resolve our concerns without the need for litigation,” he said. “Beyond this matter, we will continue to monitor companies that share board members and take enforcement actions where appropriate.” (link)

Levinson, 59, ran Genetech from 1995 until the company was acquired by Roche last April. He earned high marks as both a board member and as a CEO. An Apple spokesperson called him “an excellent director,” and a 2008 Glassdoor.com survey named him America’s “nicest boss” after his employees awarded him a rating of 93 out of 100. (In the same survey, for what it’s worth, Steve Jobs got a 90 and Eric Schmidt an 88.)

In his valedictory statement, Levinson had nothing but praise for Google.

“Working with Eric, Larry, Sergey and the whole Google team has been a remarkable experience for me,” he said. “I greatly admire what they’ve built and have no doubt that Google has a terrific future.”

So why did he pick Cupertino over Menlo Park?

In his analysis, CNBC’s Jim Goldman framed it as a one-man referendum on the future of two high-flying companies. “Everyone should face such difficult choices,” he wrote. “But I can’t help but think that knowing what he knows, who he knows, that his choice sends a clear message: Apple is the better bet; Apple offers the better opportunity; Apple poses the better proposition.”

Seth Weintraub at 9to5Mac suggests a more pecuniary motive. Google’s 2008 director compensation totaled  $189,606. Apple’s was more than three times bigger: $711,434, including a reported $8,923 worth of Apple swag.

See also:

• Who will replace Eric Schmidt on Apple’s board?
• Is Apple losing another board member?

[Follow Philip Elmer-DeWitt on Twitter @philiped]