Vice President Jeff Huber, who has led the group since 2011, is moving to Google X, the company's experimental projects group known for developing self-driving cars and the Google Glass wearable computer.
Huber, who has worked on some of Google's "most complicated issues like ads, apps, payments and geo," is "eager to work in a more startup-like environment," the company said in a statement on Thursday.
The Maps/Geo group will be folded into Google's search division, formally called Knowledge and led by Senior Vice President Alan Eustace, according to a person familiar with the matter.
Google's Commerce group, which among other things is responsible for the company's online payment product Google Wallet, will become part of the Advertising group headed by Senior Vice President Susan Wojcicki, said the person, who is not authorized to speak to the media and declined to be named.
Google, the world's No. 1 Web search engine, generated 95 percent of its revenue last year from ads.
The changes represent the most significant management reorganization since Google co-founder Larry Page became chief executive in April 2011 and streamlined the company's key products into several groups that report directly to him.
With the new changes, five main product groups instead of the previous seven will report to Page.
Page's inner circle of advisers, known internally as the L-Team, is also changing with the addition of engineering senior vice president Sridhar Ramaswmamy, according to people familiar with the matter. It was not immediately clear if Huber or Rubin were leaving the influential L-Team, which is comprised of Google's top product executives as well as finance and legal executives and is responsible for plotting Google's strategic priorities.
Shares of Google have risen 16 percent this year, as investors have gained confidence that the company is well-positioned for an industry-wide transition in which consumers increasingly use mobile phones, instead of personal computers, to access the Web.
On Wednesday Google said Sundar Pichai would take over its fast-growing Android mobile software business, replacing Rubin, who is moving to a new, yet-to-be-defined role at the company.
Google did not say what Huber's role or title would be within Google X, which is led by Google co-founder Sergey Brin.
Shares of Google were down 0.5 percent at $821.54 in late afternoon on Thursday.