"A competitive primary does not divide us, it prepares us. And we will win," Romney, the former Massachusetts governor, told cheering supporters in Tampa, Fla., Tuesday night after defeating the former House speaker from Georgia 46 percent to 32 percent.
Romney urged Republicans to focus on defeating President Barack Obama in November, declaring, "I stand ready to lead this party and to lead this nation."
Gingrich said he was undeterred by his 14-point loss and predicted he would be the Republican candidate.
"We are going to contest every state, and we are going to win and we will be the nominee in August," he told a crowd with people holding signs reading "46 States to Go."
Gingrich did not congratulate Romney for his victory, nor did he call him, The New York Times reported.
Gingrich's campaign said Monday it planned to win enough delegates in the coming months to force a brokered Republican National Convention in Tampa the week of Aug. 27.
A brokered convention happens when a single presidential hopeful does not get enough delegates through the presidential primary and caucus elections to have a pre-existing majority. At that point, nominations are decided through political horse-trading and multiple delegate votes.
Former Sen. Rick Santorum of Pennsylvania, who broke away from Florida campaigning last weekend after his daughter Bella was hospitalized with pneumonia, came in a distant third, with 13 percent of the vote. Rep. Ron Paul of Texas, who did not campaign much in Florida in favor of caucus states such as Nevada and Maine, captured 7 percent.
Santorum, who was already in Nevada for Saturday's caucuses, told supporters Tuesday night he intended to emerge as the true conservative alternative instead of Gingrich, who he said had his chance, but "it didn't work."
Santorum began running commercials in Nevada and Colorado comparing Gingrich to Obama, calling them both "cap-and-trade-loving, bailout-supporting, soft-on-immigration big-government-mandating politicians."
He said he'd deliver a speech Wednesday on the similarities between Romney's Massachusetts healthcare plan and the Patient Protection and Affordable Care Act Obama championed and signed into law.
Paul told a crowd of about 1,000 outside Las Vegas he'd called Romney to congratulate him on his victory -- then added to roaring applause that he told Romney, "I'll see you in the caucus states!"
"We've only gotten started," he said to cheers, adding, "now the counting really occurs."
Several states will hold GOP caucuses in early February. Nevada's will be Saturday and the Maine caucuses run from Saturday through Feb. 10, followed by the Colorado and Minnesota caucuses Tuesday.
After those contests, the nominating calendar has a three-week lull until Michigan and Arizona vote Feb. 28.