The decision was made by a 30-2 vote of the league owners in Houston. The Chargers were given until Jan. 16, 2017, to settle lease terms with the Rams.
The Oakland Raiders could move to Los Angeles if the Chargers do not.
The NFL would contribute $100 million to the Chargers and/or the Raiders to assist them in building new facilities in their current cities.
"The NFL owners tonight approved the return of the Los Angeles Rams starting with the 2016 season," NFL commissioner Roger Goodell said. "In 2019 they will be opening in a new stadium which we are all, as ownership, very excited about -- the kind of facility that we believe will be extraordinarily successful in the Los Angeles market. It's more than just a stadium, it's an entertainment complex."
The Rams are heading back to the L.A. area, which was their home from 1946-94.
While the new facility is being built, the Rams might play at Los Angeles Memorial Coliseum, the home of USC football and the home of the Raiders from 1982-94.
"This has been the most difficult process of my professional career," Rams owner Stan Kroenke said in a statement. "While we are excited about the prospect of building a new stadium in Inglewood, California, this is bitter sweet. St. Louis is a city known for its incredibly hard-working, passionate and proud people. Being part of the group that brought the NFL back to St. Louis in 1995 is one of the proudest moments of my professional career. Reaching two Super Bowls and winning one are things all St. Louisans should always treasure. ...
"This move isn't about whether I love St. Louis or Missouri. I do and always will. No matter what anyone says, that will never change. ...
"We would like to thank the National Football League, its owners, and the Committee on Los Angeles Opportunities for their diligence and dedication. We look forward to returning to Los Angeles and building a world-class NFL entertainment district in Inglewood."
Hall of Fame running back Eric Dickerson, who played for the then-Los Angeles Rams from 1983-87, tweeted, "Welcome Home! #LARams2016"
Chargers president Dean Spanos said in a statement, "My goal from the start of this process was to create the options necessary to safeguard the future of the Chargers franchise while respecting the will of my fellow NFL owners. Today we achieved this goal with the compromise reached by NFL ownership.
"The Chargers have been approved to relocate to Los Angeles, at the Inglewood location, at any time in the next year. In addition, the NFL has granted an additional $100 million in assistance in the event there is a potential solution that can be placed before voters in San Diego. I will be working over the next several weeks to explore the options that we have now created for ourselves to determine the best path forward for the Chargers."
Raiders owner Mark Davis said, "This is not a win for the Raiders today, but at the same time I'm really happy for Stan Kroenke. ... We'll see where Raider Nation ends up here. We'll be working really hard to find us a home. ... Don't feel bad. We'll get it right."
The Inglewood stadium, due to be built for a price of $3 billion on the site of the former Hollywood Park horse racing track, would be the NFL's largest stadium, the Times reported.
After the previous round of voting, the Inglewood project was leading 20-12 over a proposal to put two teams in a stadium in Carson, Calif., according to the Times.
Earlier Tuesday, the six-member Committee on Los Angeles Opportunities recommended a Chargers-Raiders joint relocation to the $1.7 million stadium in Carson, according to multiple reports. However, that recommendation did not appear to sway the owners.
The $1.86 billion Inglewood stadium project is backed by Rams owner Stan Kroenke. The Los Angeles Daily News reported that a Rams-only move to the stadium as sole tenant was rejected by the owners.
The Rams made the Inglewood presentation first to the owners on Tuesday followed by Carson group that included the Chargers and Raiders.
"There's momentum and commitment," said Disney CEO Bob Iger, who is part of the Carson proposal and was involved in the presentation. "But it's also complicated."
Iger said during a break in meetings that bringing the NFL to Los Angeles should be a big and bold move.
"Two is better than one (team)," he said.
Kroenke, a land developer with the second highest net worth among the NFL's 32 owners, is considered an astute businessman who could bring a winning product to California.
Committee on Los Angeles Opportunities members include owners Jerry Richardson of the Carolina Panthers, Art Rooney of the Pittsburgh Steelers, John Mara of the New York giants, Clark Hunt of the Kansas City Chiefs, Robert Kraft of the New England Patriots and Bob McNair of the Houston Texans.
Iger said the time to act was now, and that the teams had all come to a point where patience will not be tolerated by fans in existing home markets.
"At some point, there's a go/no-go date," he said. "Because these teams need to figure out where they're playing next season."