Harris wrote: "We’ve heard from our advertisers and agencies loud and clear that we can provide simpler, more robust ways to stop their ads from showing against controversial content."
The tech giant has been under pressure since a front-page story in The Times last month revealed that top brands like Mercedes-Benz, Waitrose and Marie Curie had been unwittingly funding extremists and pornography via misplaced online ads, on platforms including YouTube.
Harris said that while Google had extensive tools in place to protect advertisers from such outcomes, it could "do a better job of addressing the small number of inappropriately monetized videos and content."
He said: "We’ve begun a thorough review of our ads policies and brand controls, and we will be making changes in the coming weeks to give brands more control over where their ads appear across YouTube and the Google Display Network."
Harris, who admitted earlier this month that Google had failed to "educate" advertisers sufficiently on brand safety, has faced a barrage of criticism in recent weeks.
At a panel session at the IPA Festival of Creativity last week, WPP boss Sir Martin Sorrell called out Google for demonstrating a "lack of responsibility" on the issue.
The previous day, at the ISBA Conference, Harris was forced to fend off an attack from Saatchi & Saatchi chairman and chief strategy officer Richard Huntington that Google had fostered an environment in which "we’ve forgotten the value of context in media".