Boo Weekley made a charge on the final day in Florida, but the 34-year-old stayed bogey free for the second round running to take the title.
Victory sees Streelman claim his maiden PGA Tour title and earn an invitation to The Masters at Augusta National next month.
"I always had a dream of getting here," the PGA Tour website quotes him as saying.
"So to get this is the culmination of a lot of hard work and a lot of time spent late into the evening, and getting up early in the morning.
"I stayed really patient. It's a really tough golf course where you've got to pick your battles. It's really a dream come true."
The Duke University graduate turned professional in 2001.