The game will be played at 8:30 p.m. ET and televised by NBC.
The regular season has started on a Thursday since 2002, but the league moved this year's opener up a day to avoid a conflict with President Barack Obama's planned speech at the Democratic National Convention.
According to the league, it hasn't played a game on a Wednesday since Sept. 22, 1948, when the Rams faced the Lions.
"Who cares who we are playing; hosting the game is all that's important," Giants owner John Mara joked, knowing well that the NFL champion hosts the kickoff to the season. "It's exciting. They're one of our big rivals. We had two great games last year. The fans will be jacked up for it."
The Giants would not have been able to reach the Super Bowl if not for two critical victories over the Cowboys in the span of a month last season.
New York won in Dallas 37-34, after Jason Pierre-Paul blocked a potential overtime-forcing field goal on Dec. 11 and then capped a sweep of the Cowboys with a 31-14 victory in the regular-season finale on Jan. 1 with the NFC East division title and a playoff berth at stake.
The telecast of the Jan. 1 victory over Dallas drew 27.6 million viewers, the most for a Sunday night game. It also was the most-watched regular-season prime-time game in 15 years.
"I don't think a division game means much," Mara said. "We knew it would be a tough opponent."
It will be the first time the Giants closed one season and opened the next one in the same venue against the same opponent since 1994-95, when they hosted the Cowboys at Giants Stadium.
"That was when we were supposed to close the gap on the Cowboys," Mara said, smiling at the recollection. "And Emmitt [Smith] ran for 60-something yards on the first play."
The Giants have won five of their past six meetings against the Cowboys. This will be the second time the Giants have played in the NFL Kickoff game. They opened their Super Bowl title defense in 2008 with a 16-7 victory over Washington at home.
Information from ESPNNewYork.com's Ohm Youngmisuk and The Associated Press contributed to this report.