"I am humbled and flattered," Steinbrenner said in a statement Tuesday.
The name change was endorsed this month by the Tampa City Council and the Hillsborough County Commissioners.
"We feel this is a terrific way to honor our father's longstanding philanthropic commitment to Tampa," the owners' sons, Hank and Hal Steinbrenner, said in a statement. "Our father has always made clear how much he values Tampa's role in playing host to the New York Yankees' spring-training and the Tampa Yankees."
Hank Steinbrenner, the team's senior vice president, took over running baseball operations from his 77-year-old father last fall and Hal Steinbrenner, chairman of Yankee Global Enterprises, heads the business end.