An agreement has been reached between Formula 1's governing body and the teams to prevent a breakaway series.
The two parties had been engulfed in a bitter row over planned budgetary and technical changes for the 2010 season.
But it appears a resolution has now been found and, as part of the deal, Max Mosley has agreed not to stand for re-election as president of the FIA.
"There will be no split, there will be one F1 championship. We have agreed to a reduction of costs," said Mosley.
"The objective is to get back to the spending levels of the early 90s within two years."
F1 supremo Bernie Ecclestone added that he was "very happy common sense has prevailed" following a meeting of 120 members of the FIA in Paris aimed at resolving the crisis.
Ferrari chief president Luca di Montezemolo, head of the Formula One Teams Association (Fota), added: "I think the decisions we have shared this morning are important. We will have the rules of 2009, same rules for everybody.
"I think [Max Mosley] has done a very good fix of the problem. When you have reached an agreement everyone has to help in the same way."
Ahead of the meeting, Mosley had insisted that he would not step down as part of any potential agreement and might even seek re-election as head of world motor sport.
He hit out at what he described as "wholly unjustified criticism" of the FIA, adding: "It is for the FIA membership, and the FIA membership alone, to decide on its democratically elected leadership, not the motor industry and still less the individuals the industry employs to run its F1 teams."
However, it appears Mosley has now agreed to move aside when his fourth term as FIA president ends in October, saying: "I will not be up for re-election, now we have peace."
Furthermore, writs that had been threatened against Ferrari and the other teams in Fota - McLaren, BMW Sauber, Renault, Toyota, Red Bull Racing, Toro Rosso and Brawn GP - are likely to be shelved.
"Fota's public stance before this meeting was that they weren't in the mood for negotiation or compromise - and if we take that on board, the fact that they've got their way today must be seen as something of a capitulation by the FIA," reported BBC Five Live's David Croft.
I always thought there wasn't much between us, now we've agreed there isn't
FIA president Max Mosley
And that is a view shared by Ferrari, who issued a statement reading: "The FIA's World Motor Sports Council has approved all Fota's proposals."
It added: "The objective is to avoid continuous changes decided by one person alone."
However, Mosley sought to play down suggestions he had bowed to Fota's requests, telling BBC Sport: "I know it's an old cliche but everybody's won.
"What we wanted was to get new teams into F1. We've got new teams in, which we haven't been able to do for 10-15 years, and at the same time got costs down so independent teams are profitable
"If they're happy with what they (Fota) have got, fine, I've won what I wanted.
Report - Mosley agrees to stand down
"As far as I'm concerned the teams were always going to get rid of me in October, well they still are. Whether the person who succeeds me will be more to their liking remains to be seen."
The agreement ends two months of wrangling since Mosley announced after a World Council meeting at the end of April that a voluntary £40m budget cap would be imposed from next season - a plan that prompted a rebellion from eight teams, with Fota announcing on Thursday they were planning a rival series.
But the new agreement ends that threat, while still maintaining the "financial viability" of teams which had been targeted with the initial budgetary restrictions.
Mosley explained: "There is no budget cap because costs will come down to the levels of early 1990s in two years - it's a different way of doing the same thing. I always thought there wasn't much between us, now we've agreed there isn't."
As part of the agreement, existing teams must help new outfits - Campos, US F1 and Manor - with their engines and chassis.
We look forward to working with the FIA Senate to achieve a prosperous and exciting future for Formula 1
Toyota president John Howett
Toyota president John Howett, the vice-chairman of Fota, hailed the unity of the teams even though Williams and Force India broke ranks and submitted unconditional 2010 entries earlier this month.
"This has been a challenging period," he said.
"But thanks to the unity of the Fota teams and the foresight of the World Motor Sport Council members we have achieved the right result for Formula 1," he said.
"We look forward to working with the FIA Senate to achieve a prosperous and exciting future for Formula 1 and its millions of fans around the world."
BBC sports news correspondent James Munro, reporting from Paris, said: "It's come as a bit of a surprise, given that Fota was planning to meet in Bologna on Thursday to discuss plans for the breakaway championship.
"But what we got today after a meeting of World Motorsport Council was an impromptu press conference and Mosley began by saying there will be no split, there will be one championship.
"He said that over the course of the negotiations he had been able to secure guarantees from the teams who were threatening to break away that they would try to rein back the levels of their spending to the levels they were spending in the early 90s.
F1 now has stability - Di Montezemolo
"It was him that had come up with the idea that next season all teams would have a budget cap of about £40m, but there has clearly been a trade-off as he has also agreed to do what he says was always the plan - stand down as president of the FIA this October."
It is not the first time Mosley has promised to stand down as FIA president - in June 2004, he announced he would stand down from his position in October of that year, only to rescind his decision a month later and secure re-election.
But he was adamant that with his 70th birthday approaching, and with the row finally settled, there was no way he would be having a change of heart this time.
"As long as the teams behave themselves I will be gone," he said. "A deal is a deal and if it is not stuck to you sometimes have to reconsider things. However, I have absolute confidence that this resolution will be stuck to."
Fota was expected to address the media at a press conference on Thursday.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.