The 29-year-old sous chef scooped the head chef job at LA Market and an annual salary of $250,000 over fellow finalist Russell Kook II on Wednesday night's season finale.
Sivley, a mother from Fort Worth, TX, will also act as spokesperson for Rosemount Winery.
"I fought and I fought and I fought," she said after the result. "I'm so thankful. This was a huge sacrifice. Missing my son's first birthday, his first steps. It's absolutely worth it to make his life better."
Gordon Ramsay, who had told both chefs that their final scores had been "incredibly close" and he wished he could have given out two jobs, said that Nona had improved every week and had a "phenomenal palate" and a "real passion" for cooking.
The final challenge had seen Nona and Russell joined by former contestants as they took on head chef responsibilities at Hell's Kitchen. Nona was partnered with Gail, Melissa, Boris and Trev, while Russell (who got to pick first after winning an earlier challenge) was teamed with Jillian, Sabrina, Vinny and Rob.
Nona chose to serve a Southern-inspired menu including baby beet salad, pan-seared halibut and rib-eye with red wine sauce, while Russell opted for a European-themed menu of scallops, goat cheese ravioli and pan-seared filet mignon. Both chefs managed to retain control of their kitchens despite encountering problems during service, including communication issues with their teammates and having to ensure the quality of every dish being served.
Despite handing the win to Nona, Gordon told Russell that he had done an "amazing job" and should keep up the good work. Russell, however, admitted privately that he was "pissed" by the result.
"I'm not happy at all," he said. "I chose the team I wanted and I thought they would help me win. They helped me lose. Thanks a lot guys. You will never get a job in any city I work. I will definitely blackball you guys because you f**ked me so royally tonight."
Russell had won an earlier challenge, which saw the finalists having to prepare five dishes in just one hour for some of the "most distinguished" members of the Los Angeles culinary community. They were also treated to a helicopter tour of the city with Gordon.
Hell's Kitchen airs on Fox