Eich moved up to CEO from his previous job as chief technology officer for the nonprofit organization, which operates Mozilla Corp. as a commercial entity. Mozilla Corp. is the maker of the Firefox browser.
Mozilla's board appointed Eich on Monday, with the promotion effective immediately. Former acting-CEO Jay Sullivan has left to "pursue new opportunities," according to Mozilla.
"Brendan brings Mozilla's founding vision and boldness to our current initiatives," the company said in a blog. "These traits are a unique asset as Mozilla brings openness and choice through new initiative such as Firefox OS and cloud services."
Eich founded Mozilla with Mitchell Baker, the chairman of the Mozilla Foundation, in 1998 as a project spun off by Netscape, the browser company that was eventually sold to AOL for $10 billion at the height of the dot-com boom.
Mozilla released its first Firefox browser in 2004.
In April 2013, the organization's previous CEO, Gary Kovacs, announced that he was stepping down. Kovacs is now chief executive of antivirus vendor AVG Technologies.
In a blog of his own, Eich did not reveal any major changes in Mozilla's strategy, which increasingly has focused on Firefox OS, the lightweight browser-based mobile operating system.
Firefox OS has aimed at the very low end of smartphones, the part of the market now dominated by forked versions of Android and handset manufacturers based in China. At Mobile World Congress last month, Mozilla and China-based chip maker Spreadtrum unveiled a chipset designed for ultra-cheap Firefox OS-powered smartphones that could be priced as low as $25.
One analyst drew a comparison between Mozilla's choice for its latest CEO and moves made last month by Microsoft, its much bigger browser rival.
"It is interesting that we are seeing Mozilla go inside for its CEO search, much like its arch-rival Microsoft did a few weeks ago, and also interesting that both have returned to their tech founders for strategy," said Al Hilwa of IDC.
About Microsoft, Hilwa was referring to the company's selection of insider Satya Nadella as the new chief executive, and the decision by co-founder Bill Gates to leave his board chairman role to advise Nadella on product and technology issues.
"Mozilla has been an amazingly successful organization, but the changes in client-side computing taking place present interesting strategic challenges," Hilwa continued in an email reply to questions. "We are shifting to a more fragmented client-side environment where Web browsing is tied to devices and this is a challenge for an independent browser maker. Mozilla has been forging a market for its own mobile OS and has several irons in the fire."
"Brendan is a strong technical leader and it may be what is needed to navigate the rough waters going forward," Hilwa said.
Firefox has a usage share of about 17.7% among desktop browsers, according to the latest data from Internet analytics company Net Applications.
Gregg Keizer covers Microsoft, security issues, Apple, Web browsers and general technology breaking news for Computerworld. Follow Gregg on Twitter at @gkeizer, on Google+ or subscribe to Gregg's RSS feed . His email address is email@example.com.