Android phone and tablet users in the European Union are to be given a chance to install one of Google's rivals as default search provider.
But to be offered as an option, search firms will have to compete over what to pay Google if users select them.
The decision to offer a choice when setting up devices comes after Google was fined heavily by the European Commission for abusing its position.
But one competitor has warned that users might lose out as a result.
"If the highest bidder wins the contract and not the best search engine, then the user is the biggest loser," said Dr Marc Al-Hames, chief executive at Cliqz, a search firm based in Munich, Germany.
"The choice should be about selecting the most private or innovative provider."
Google was fined €4.3bn ($4.8bn; £3.72bn) for abusing its market position in July 2018.
It has now said that, beginning in 2020, Android users in the European Economic Area (EEA) - a broader market than the EU - will be shown a screen giving them a choice of four possible search providers to use as default on their devices.
One of these options will always be Google but the other three will be chosen from the highest-bidding rival search firms.
A separate bidding process will exist for each country.
"It's correct that the new screen will be based on an auction," a Google spokeswoman told the BBC.
Google will still allocate a total of three search providers for users to choose from, even if they don't all meet the minimum criteria.
"The auction winners, and Google, will be ordered randomly in the choice screen," the tech giant said on a web page about the change.
The new search provider choice screen will appear only on Android phones where Google's own search app is pre-installed.
Earlier this year, Google announced it would make changes to how its search results within the EU were displayed.
This involved directing users to rival price-comparison websites and merchants selling products.