In a joint statement, the Chargers and Raiders said they have been working for many years in their home markets to find stadium solutions and that they remain committed throughout 2015 to try to seek publicly acceptable solutions to the stadium issues in their current cities.
However, according to the statement, the two teams also will continue to work in Carson to preserve their options in the event that efforts in their local markets fail.
Both teams have kept the NFL committee handling the possible relocation of teams to Los Angeles informed of their efforts.
"We are pursuing this stadium option in Carson for one straightforward reason: 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 teams said in the joint statement.
The agreement was earlier reported by the Los Angeles Times.
A source involved in the negotiations told ESPN.com's Arash Markazi that the Chargers came to Carson officials first with the stadium proposal nine months ago and that the Raiders later joined the talks, which intensified after St. Louis Rams owner Stan Kroenke announced plans in January to build an 80,000-seat stadium in Inglewood.
The Chargers and Raiders are partnering with a local development group. The site of the proposed stadium is a 168-acre parcel near the 405 freeway in Carson. The city is 15 miles south of downtown Los Angeles and is home to Major League Soccer's Los Angeles Galaxy.
The group intends to start a petition drive for a ballot initiative to get voter approval to build the stadium.
This latest development comes a month and a half after an announcement in which a developer and a company operated by Kroenke unveiled plans to build a stadium on land he owns near Hollywood Park.
In addition, a plan for an NFL facility in downtown Los Angeles remains alive. The would-be 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.
Los Angeles has not had an NFL team since the Rams and Raiders departed for St. Louis and Oakland, respectively, in 1995.
The Chargers, the Raiders and the Rams are teams that could potentially relocate to the lucrative Los Angeles market in the near future. All three teams can terminate their leases at the end of the 2015 season.
If the Chargers and Raiders move to Los Angeles after the 2015 season, they would have to play in a temporary home for at least two seasons while the stadium in Carson is being built.
Both teams would prefer to play at the Rose Bowl because it is more NFL-ready than the Los Angeles Coliseum, a source told Markazi. The Rose Bowl recently underwent $182 million in improvements, including new suites, club seats and refurbished locker rooms, while USC, which took control of the Coliseum, is still unsure of renovation plans.
In addition, since both the Chargers and Raiders play in the AFC West, one team would have to move to the NFC, likely switching places with an NFC West team. That decision ultimately would be the NFL's, but a source told Markazi that a move to the NFC would not deter the Chargers or Raiders from making the move to Los Angeles.
In January, the Chargers denied speculation emanating from St. Louis that the team had an agreement in place for a new stadium in Los Angeles.
The Chargers have tried unsuccessfully for 14 years to build enough momentum to get a new stadium in their home city. San Diego Mayor Kevin Faulconer appointed a nine-member stadium advisory group to come up with a recommendation for a stadium site and a financing plan last month, but the team has viewed that effort as a futile, last-ditch attempt to keep the team in San Diego.
"It's now abundantly clear that while we have been working here in San Diego to create a plan for a new stadium, the Chargers have for some time been making their own plans for moving to Los Angeles," Faulconer said in a statement Thursday night. "This would amount to abandoning generations of loyal Chargers fans. Despite this news, we are going to continue our efforts to develop a viable stadium solution."
Adam Day, chairman of the volunteer stadium task force, said Thursday's announcement 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," he said.
The Raiders currently play in the aging Oakland Coliseum. The rundown stadium has had sewage and electrical problems in the past year, and now is the only stadium in the U.S. used as the home for both an NFL and a 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 on the city's north riverfront.
"Our focus is 100 percent committed to keeping the Rams here in their home of St. Louis and ensuring that we remain an NFL city for generations to come," said former Anheuser-Busch president Dave Peacock, who is heading the effort to keep the Rams in St. Louis. "We are very encouraged and thrilled with the progress we've made."
All three teams have Los Angeles ties. The Rams called the area home from 1946 to 1994, the Raiders were there from 1982 to 1994 and the Chargers played their inaugural 1960 season in L.A.
ESPN.com's Arash Markazi and The Associated Press contributed to this report.
Raiders, Chargers Could Share LA Stadium
Chris Mortensen talks about reports that the Raiders and Chargers are working together to build and share a new stadium just outside Los Angeles.