The NFL said Monday the Giants will play on Sunday afternoon, Sept. 12, and the Jets will host a Monday night game the next day.
Opponents have not been announced; the full league schedule usually is released in early April.
"After extensive discussions with both teams, we have come up with what we believe is a unique approach for celebrating the opening of the new Meadowlands Stadium," commissioner Roger Goodell said.
The issue became somewhat contentious when the Jets announced on their Web site that a coin toss conducted by the league would determine which team opens the $1.7 billion stadium. The teams split the cost on the replacement for Giants Stadium, which they both called home since 1984.
But the league never confirmed such a decision until Monday, when it said Goodell did flip a coin for which team would play Sunday.
The Giants won, and the Jets are not happy with the process.
"An NFL coin toss has a few fundamental elements that are missing here, most notably the presence of the teams involved," Jets owner Woody Johnson said in a statement. "That's how it's always done in the league, whether it's determining the order of the draft or deciding who's going to kick off the game.
"When the issue of which team would be hosting the first regular-season game could not be resolved on the merits, I suggested a coin toss as the fairest way to resolve this issue. The league rejected that idea. Then, I was told on Friday that a coin toss had taken place at the league office and that the Jets had lost. We rejected a process in which neither team was present. The league departed from our time-honored tradition and declined the opportunity to set the matter straight with a transparent process."
The Giants had no complaints.
"We look forward to playing the first regular-season game ever in the new stadium," Giants spokesman Pat Hanlon said. "We have a great new home, and it's right next door to Giants Stadium, a building that housed our three Super Bowl championship teams. We look forward to building the same legacy for our new stadium, and it starts on Sept. 12."
Goodell said the teams' owners were passionate about being the first to play at home. He concluded that the fairest resolution would be to play both teams at home on the opening weekend and to use the coin flip.
"We have no further comment beyond our statement of yesterday," NFL spokesman Greg Aiello said.
The Jets will host the first NFL game at the new stadium during the preseason in August.
Only once have the Giants and Jets opened a regular season on the same weekend at Giants Stadium. In 1991, the Jets played Tampa Bay on Sunday, Sept. 1, and the Giants hosted the 49ers on Monday night, Sept. 2.
Information from The Associated Press was used in this report.