The term Manifest Destiny apparently appeared in print for the first time in 1839, and was most famously used by journalist John O' Sullivan in 1845, where he argued in favor of the annexation of Texas and Oregon. The concept, however, is ingrained in American ideological thought.
From wikipedia: "Historian William E. Weeks has noted that three key themes were usually touched upon by advocates of Manifest Destiny:
1. the virtue of the American people and their institutions; 2. the mission to spread these institutions, thereby redeeming and remaking the world in the image of the U.S.; and 3. the destiny under God to accomplish this work.
The origin of the first theme, later known as American Exceptionalism, was often traced to America's Puritan heritage, particularly John Winthrop's famous "City upon a Hill" sermon of 1630, in which he called for the establishment of a virtuous community that would be a shining example to the Old World. In his influential 1776 pamphlet Common Sense, Thomas Paine echoed this notion, arguing that the American Revolution provided an opportunity to create a new, better society