The victory was the Dutch driver's third of the season, and second in a row, and he made it happen with a crucial overtake around the outside on Sainz at the start to seize second place before blasting past Leclerc on the ninth of the 57 laps.
Media reports have valued the new deal at 40-50 million euros ($44-$55 million) a year.
Lewis Hamilton, beaten this year on the last lap of the last race, did not attend the event at the Louvre museum in Paris.
Red Bull rival Max Verstappen ended the Briton's quest for an unprecedented eighth F1 title with a safety-car aided, last-lap pass for championship glory at the season-ending Abu Dhabi GP.
Verstappen passed title rival Lewis Hamilton on the last lap. After a record 22 races, Verstappen had 395.5 points to Hamilton's 387.5.
Seven-time world champion Hamilton was second for Mercedes, holding off Red Bull's Sergio Perez who became the first Mexican to stand on his home podium.
The win was Verstappen's eighth of the season, and first in America, but one he had to sweat for in front of a sell-out 140,000 crowd.
The 24-year-old Red Bull racer also gave the seven-time world champion, the most successful driver of all time, a single digit salute as the Mercedes accelerated away on a hot and humid Texas afternoon at Austin's Circuit of the Americas.
Red Bull's Max Verstappen finished second to take back the Formula One world championship lead.
The 23-year-old dominated from pole position to take the chequered flag in the first Dutch GP for 36 years, beating Mercedes' seven-time world champion Lewis Hamilton and Valtteri Bottas.