The proposed $1.7-billion stadium would be in Carson, 15 miles south of downtown Los Angeles and home to the Los Angeles Galaxy soccer team.
The statement says the teams have tried and failed for years to find stadium solutions in Oakland and San Diego, and without new agreements in those cities their hands will be forced.
"We are pursuing this stadium option in Carson for one straightforward reason," the statement says. "If we cannot find a permanent solution in our home markets, we have no alternative but to preserve other options to guarantee the future economic viability of our franchises."
The plan creates the odd prospect of divisional rivals suddenly sharing a home field, and of Los Angeles having two NFL teams after going two decades with none.
And it takes the muddled issue of the NFL's return to Southern California and makes it downright messy, with at least three viable stadium plans in the works.
St. Louis Rams owner Stan Kroenke is part of a joint venture to build an 80,000-seat stadium at the site of the former Hollywood Park horse track just 10 miles from Carson in Inglewood.
And a plan remains alive for an NFL facility in downtown Los Angeles. That stadium known as Farmers Field, until recently the leading candidate for the NFL's return, now becomes a long shot with multiple competitors and no clear team attached.
Earlier this month, the NFL sent a memo warning teams that the league itself will be behind any decision to move to Southern California, and established a committee of owners to review the options.
The Chargers and Raiders statement says they will respect and adhere to the guidelines the league laid out.
The teams said they plan to work in good faith through 2015 to find new agreements to stay in their current homes, where they are both in year-to-year leases and both have sought public funding that has been hard to get.
The Chargers' talks with San Diego City Hall to replace the nearly 50-year-old Qualcomm Stadium have grown increasingly contentious. Mayor Kevin Faulconer appointed an advisory group earlier this month to recommend a site and financing plan for a new stadium that can go on the November 2016 ballot. But Chargers' attorney Mark Fabiani told the group that there may not be a publicly acceptable solution to the problem and warned them against using the team for political advantage.
The head of the mayor's group Adam Day said the new plan came as a "complete surprise."
"While it's disappointing to hear the Chargers are moving forward with plans in Los Angeles, we remain committed to finding a solution in San Diego," Day said in a statement.
The Raiders' even older Oakland Coliseum has had sewage and electrical problems and is now the only stadium in the US used as the home for both an NFL and Major League Baseball team, the Oakland Athletics. The team wants to build a new stadium at the site but talks with the city have shown little progress.
Oakland Mayor Libby Schaaf said she spoke Thursday night with team president and CEO Marc Badain, "and he continued to assure me that the Raiders' first priority is to stay in Oakland in a new stadium."
Schaaf said she wants to be "a responsible steward of the public dollar, to keep my sports teams and" to redevelop the neighborhood around the Coliseum. She added: "I am committed to not putting public dollars into stadium construction."
The Rams have been in a similar struggle with St. Louis, but have made progress with a burgeoning plan for a 64,000-seat stadium there on the city's north riverfront.
All three teams have Los Angeles ties. The Rams called the area home from 1946 to 1994, the Raiders were here from 1982 to 1994 and the Chargers played their inaugural 1960 season in LA.