Final answer:
In the Adams-Onís Treaty of 1819, the United States gained full control of Florida from Spain by renouncing its claims to Texas, while also settling American financial claims against Spain.
Step-by-step explanation:
The United States acquired all of Florida in the Adams-Onís Treaty because it agreed to give up its claims on Texas. This diplomatic agreement, concluded in 1819, was primarily negotiated by Secretary of State John Quincy Adams and the Spanish minister Luis de Onís. The treaty granted the United States full control over Florida, while in exchange, the U.S. renounced its territorial claims to Texas, at least temporarily.
Furthermore, as part of the Adams-Onís Treaty, Spain also relinquished its claim to the Oregon territory. The United States, in turn, assumed the responsibility for settling $5 million in claims against Spain by American citizens. This acquisition of Florida by the U.S. was significant as it marked further territorial expansion and a redefinition of the nation's borders.