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.