Final answer:
The United States settled the Oregon boundary in 1846 through a treaty with Great Britain, agreeing on the 49th parallel as the boundary line. President James K. Polk initially supported a more aggressive stance but ultimately condoned the compromise for strategic reasons.
Step-by-step explanation:
Settlement of the Oregon Boundary
The year the United States settled the Oregon boundary was 1846. This was the result of negotiations between the United States and Great Britain, driven by the burgeoning concept of Manifest Destiny and the surge of American settlers moving westward on the Oregon Trail. President James K. Polk, a fervent expansionist, campaigned with the slogan "Fifty-four forty or fight!" proclaiming the desire to take control of the entire Oregon Territory.
Despite this, the practical outcome was the acceptance of the 49th parallel as the dividing line, established in the June 1846 treaty with Great Britain. This decision allowed the United States to acquire territory that would contribute to the balance of free and slaveholding states at the time and brought into the fold the Pacific Northwest, including a valuable deepwater port at Puget Sound.