The Chip Ganassi driver raced conservatively for a comfortable second behind American Ryan Hunter-Reay with Rossi finished seventh.
"Man, this is so awesome I can't believe it's actually happened," Dixon said. "You always doubt these situations so much that they're never going to happen."
Dixon won three of the 17 races on this year's schedule and had 13 top-fives.
He previously won the IndyCar championship in 2003, 2008, 2013 and 2015.
American A.J. Foyt holds the record with seven open-wheel titles on the U.S. circuit between 1960 and 1979.
Dixon's task on Sunday was made considerably easier after Rossi's early trouble. Rossi made contact with the back of team mate Marco Andretti's car, which resulted in a damaged front wing and forced him to pit.
He dropped to last and while he got back into the race later under a yellow flag he could not threaten the leaders.
"I wish I could replay that a million more times," said American Rossi, a former Formula One driver.
"The team did a great job to get me back on the road to recovery after the mistake I made.
"A huge congratulations to Scott. He's a five-times champion for a reason. It was a pleasure to race against him all year."
Rossi finished second in the season-long standings, with Australian Will Power third and Hunter-Reay fourth.
"Flawless year. Very deserved champion," Power said of Dixon.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury/Peter Rutherford)
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