Google is set to launch new tools to limit the use of tracking cookies, a move that could strengthen the search giant’s advertising dominance and deal a blow to other digital-marketing companies, according to people familiar with the matter.

After years of internal debate, Google could as soon as this week roll out a dashboard-like function in its Chrome browser that will give internet users more information about what cookies are tracking them and offer options to fend them off, the people said.

This...