Joint control worked for over a decade and a half but ultimately, the parties decided that joint occupancy wasn't working well so they set about to divide Oregon.
The 1844 Democratic presidential candidate James K. Polk ran on a platform of taking control over the entire Oregon Territory and used the famous campaign slogan, "Fifty-four Forty or Fight!" (after the line of latitude serving as the northern boundary of Oregon at 54°40'). Polk's plan was to claim and go to war over the entire territory for the United States.
Polk won the election with a popular vote of 1,337,243 to Henry Clay's 1,299,068 (the electoral vote yielded Polk 170 votes vs. 105 for Clay).
Through negotiations with the British after Polk's inauguration, the boundary between the U.S. and British Canada was established at 49° with the Treaty of Oregon in 1846. The exception to the 49th parallel boundary is that it turns south in the channel separating Vancouver Island with the mainland and then turns south and then west through the Juan de Fuca Strait. This maritime portion of the boundary wasn't officially demarcated until 1872.
The boundary established by the Oregon Treaty still exists today between the United States and independent Canada.