Hendrick said Elliott also would drive in five Cup races this year in a No. 25 Chevy in preparation of his full-time move into stock-car racing's premier series.
Elliott, son of former Cup champion Bill Elliott, last year won the championship in NASCAR's second-tier Nationwide Series, now called the NASCAR Xfinity Series, becoming the youngest title winner in history in one of NASCAR's three national series.
His promotion came one week after the 43-year-old Gordon, a four-time champion who initially reached the Cup series at age 21, said he would stop racing full time after this season.
Elliott's promotion also came one day before his father was to be inducted into the NASCAR Hall of Fame.
"Chase brings the kind of intangibles that make him the total package as a driver," team owner Rick Hendrick said in a statement, adding that Gordon's crew chief, Alan Gustafson, would assume the same role with Elliott.
"Not only is he a special talent inside the race car, but there's a natural combination of competitiveness, work ethic and smarts that you rarely see," Hendrick said.
Elliott said he was "extremely grateful to Mr. Hendrick," adding in a statement that "my parents especially have believed in me every step of the way, and I know this wouldn't be possible without all the sacrifices they've made to focus on my racing career."
Elliott's five Cup races this season are scheduled at Martinsville, Va.; Richmond, Va.; Charlotte, N.C.; Darlington, S.C., and Indianapolis.
Follow @PeltzLATimes for more motor racing news