In addition, the prime minister said possessing online pornography depicting rape would become illegal in England and Wales - in line with Scotland.
Mr Cameron warned in a speech that access to online pornography was "corroding childhood".
The new measures will apply to both existing and new customers.
Mr Cameron also called for some "horrific" internet search terms to be "blacklisted", meaning they would automatically bring up no results on websites such as Google or Bing.
He also warned he could have to "force action" by changing the law and that, if there were "technical obstacles", firms should use their "greatest brains" to overcome them.
In his speech, Mr Cameron said family-friendly filters would be automatically selected for all new customers by the end of the year - although they could choose to switch them off.
And millions of existing computer users would be contacted by their internet providers and told they must decide whether to use or not use "family-friendly filters" to restrict adult material.
The filters would apply to all devices linked to the affected home Wi-Fi network and across the public Wi-Fi network "wherever children are likely to be present".
Customers who do not click on either option - accepting or declining - will have filters activated by default, Tory MP Claire Perry, Mr Cameron's adviser on the sexualisation and commercialisation of childhood, told the BBC.
The UK's biggest internet service providers have agreed to the filters scheme meaning it should cover 95% of homes.
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