The so-called "right to be forgotten" was upheld by Europe's top court on May 13 when it ordered Google to remove a link to a 15-year-old newspaper article about a Spanish man's bankruptcy.
"This week we're starting to take action on removals requests that we've received," a Google spokesman said on Thursday. "This is a new process for us. Each request has to be assessed individually and we're working as quickly as possible to get through the queue."
Google received over 41,000 requests over four days after it put up an online form allowing Europeans to request that search results be removed.
Internet privacy concerns shot up the agenda last year when former U.S. National Security Agency contractor Edward Snowden revealed details of mass U.S. surveillance programmes involving European citizens and some heads of state.
The EU executive has been critical of several major U.S. web companies, such as Facebook and Google, over their handling of swathes of personal data. National governments recently moved towards extending Europe's strict data protection rules to all companies, not just European ones.