On December 27, 1845, John L. O'Sullivan wrote an influential editorial for the New York Morning News that is credited as the first use of "manifest destiny" to describe and justify the continental expansion of the United States. O'Sullivan wrote:
And that claim is by the right of our manifest destiny to overspread and to possess the whole of the continent which Providence has given us for the development of the great experiment of liberty and federated self-government entrusted to us.Article in which John L. O'Sullivan first used the term Manifest Destiny, reprinted in a newspaper Wed, Sep 10, 1845 – 1 · Mississippi Democrat (Carrollton, Mississippi, United States of America) · Newspapers.com
However, O'Sullivan certainly didn't coin the phrase, despite the fact that he is often credited with it.
For example, the editor of the Brooklyn Daily Advertiser used the phrase in connection to Louis Napoleon in 1840. It seems the future Emperor of France had been caught at a brothel (presumably in New York City), and the Daily Advertiser used "manifest destiny" to describe Louis's fate:
Even earlier, the term was being used to describe one group conquering another. In an address to the Massachusetts Charitable Mechanic Association in 1824, Alphaeus Cary used the term "manifest destiny" to describe the spread of the Roman Empire: