Ferrari have broken ranks with the teams planning a breakaway series and committed to Formula One until 2012.
Ferrari were key players in the battle for the future of F1
The world champions have signed an extension of the Concorde Agreement that governs the running of the sport.
F1 boss Bernie Ecclestone said he was "delighted... the future of F1 has now been stabilised".
Ecclestone hopes the move will end any major threat to F1's future from the Grand Prix World Championship (GPWC), which is threatening a breakaway.
Ecclestone told BBC Sport in an exclusive interview that Ferrari had signed a new version of the Concorde Agreement that resolved many of the grievances held by the GPWC, which was led by Ferrari, DaimlerChrysler (Mercedes), Renault and BMW (Williams).
They were asking for a greater share of F1's revenues and more say in the running of the sport.
Ecclestone said: "The parts of the Concorde Agreement they were concerned with will be dealt with and they are going to get more money."
He said he was offering the teams an extra $500m (£267m) over the next three years.
The other teams had not signed yet, he said, but they were aware of the new terms.
"The people I have spoken to are happy - about four or five of them," Ecclestone added.
"At the moment, when I've spoken to them on the phone, the answer was: 'It's positive.'
"Having thought about everything and seen whether they can do better or worse, that's how it is."
Later on Wednesday Ecclestone was quoted by Reuters saying he had spoken to all the teams bar Jordan.
"They are all relieved," he said. "Their main concern is that the technical regulations don't keep changing. That's what's cost them a fortune."
It has long been accepted that whichever side won Ferrari's commitment would win the battle for the future of F1.
That is because Ferrari's prestige as the most famous and well-supported team in the sport would guarantee the championship they were involved in would have the biggest following in the event of any split.
Ecclestone has pulled off the latest in a long line of political coups
Minardi team owner Paul Stoddart told the Reuters news agency: "I don't think it's the end of the GPWC but it is the end of them starting a separate championship."
He described Ferrari's decision as "a rather major coup on Bernie's part".
FIA president Max Mosley said: "We are very pleased to have reached this agreement with F1's commercial rights holder (Ecclestone) and the oldest team in the championship.
"The agreement is significant because it will ensure the future development of the FIA's most important championship."
Ferrari president Luca di Montezemolo added: "It is important that the FIA, FOM (Formula One Management) and Ferrari have put out a strong message of stability for the future of F1.
"The agreement is in line with what Ferrari had hoped for, for a long time."
Ecclestone played down the seriousness of the GPWC's plans.
"There's never been a battle," he said.
"Every time we've had a Concorde Agreement - and I've been involved with all of them - there's always been something going on and somebody doing something, trying to do the best they can for themselves. No problems."
But he admitted that Ferrari's decision would mean the FIA F1 World Championship would remain the leading motorsport championship into the foreseeable future.