He is one of a number of high-profile contributors who have written articles for the week, which is run by the Newspaper Society from 9-15 May to celebrate the strength of the local and regional press.
Hundreds of papers across the country have been taking part in Local Newspaper Week, highlighting their campaigning work and the role they play in the community.
In Mr Cameron’s piece, he said local newspapers were important for democracy and in helping to build a stronger society.
He wrote: “For decades, local newspapers have faced fierce competition. First there was the radio, then television, now of course, the internet. But despite all these challenges, they continue to play a vital role and that’s testament to the extraordinary creativity and versatility of all those people who work in local media.
“Local newspapers are hugely important to our country – for two good reasons. First, they strengthen our democracy, holding the powerful to account.
“Whereas national newspapers can focus on the bigger picture, it’s local papers that often really analyse the detail of what central and local government is doing and the impact their policies have on the ground.
“Second, local papers are hugely important in helping to build a bigger, stronger society. There is a massive gap between the state on the one hand, and the individual on the other, and local papers help fill the space in between, galvanising readers into action.”
Other people who have contributed articles include Michel Roux Jr, Peter Preston and Julia Bradbury.
To mark the week, papers including the Liverpool Echo, Ipswich daily the Evening Star, the Hartlepool Mail, Newcastle’s Evening Chronicle and the Halifax Courier have highlighted the campaigning work they have done for good causes in their areas.
And the Huddersfield Daily Examiner informed readers about how it was adopting multimedia reporting in a feature.