NBC will televise the game, which will kick off at 8:30 p.m. ET.
The NFL announced last month that the season opener would be held on a Wednesday night instead of the traditional Thursday night to avoid a conflict with President Obama's speech at the Democratic National Convention.
"Who cares who we are playing? Hosting the game is all that's important," Giants owner John Mara jokingly said Monday at the NFL Annual Meeting in Palm Beach, Fla., knowing full well that the Super Bowl champion hosts the kickoff to the season.
"It's exciting," Mara said of opening the season against the Cowboys. "They're one of our big rivals. We had two great games last year. The fans will be jacked up for it."
The Cowboys' last game also was at the Meadowlands, where the Giants prevailed 31-14 to win the NFC East title. That was the second of six consecutive victories for New York that culminated in a Super Bowl XLVI victory over the New England Patriots.
The telecast of that victory over Dallas averaged 27.6 million viewers, the most ever for a Sunday night game. It was the most-watched regular-season prime-time game in 15 years.
The Associated Press contributed to this report.