MIAMI — Gov. Rick Scott made official on Monday what Floridians have suspected for months: He is running for the United States Senate against Bill Nelson, the incumbent Democrat, in a premier race that will return the nation’s largest swing state to its familiar role as the political vortex of a tumultuous election year.

“This is going to be a lot of fun,” Mr. Scott, wearing his usual Navy baseball cap, said in an announcement on Facebook Live from an Orlando construction company, before embarking on the kind of statewide tour that has become his signature over two terms as governor. “We’re going to make sure that Washington works for us.”

With his formal entry into the campaign, Mr. Scott, a 65-year-old Republican, made Florida a centerpiece of the midterm elections, featuring one of the most expensive Senate races in the country, as well as an open governor’s race and up to a half-dozen competitive House races. The contest between Mr. Nelson and Mr. Scott alone is expected to cost $100 million, or even much more, chiefly from spending on television advertising across Florida’s 10 broadcast media markets. Mr. Scott, a multimillionaire former health care executive, invested millions of his own money into his successful campaigns for governor in 2010 and 2014.

The Florida Senate battle will be a microcosm of national Republicans’ fight to keep control of Congress under President Trump, whose policies and demeanor have invigorated Democratic voters. Mr. Nelson is one of 10 Democratic senators seeking re-election in states Mr. Trump won in 2016, and Republicans have repeatedly bested Democrats in most statewide Florida midterm races since 2006 — though Mr. Nelson’s win was one of two Democratic victories that year.