The agreed merger will create the world's fourth largest oil major behind Exxon-Mobil, Shell and BP Amoco with a market capitalisation of $100bn, output of 2 million barrels of oil and gas a day and oil reserves of 2.6 billion barrels.
Philippe Jaffre, the Elf chairman, who had reacted to TotalFina's initial hostile bid in July by launching a rival offer - the "Pacman defence" - will step down once the offer goes through.
"There is a time to say `No' and there's also a time to say `Yes', without reticence, without reserve and without regrets," Mr Jaffre told a Paris news conference.
Speculation had been growing in recent days that the two oil groups were inching towards an amicable deal, based on an improvement in TotalFina's terms. Under the new terms it is offering 19 of its shares for every 13 Elf shares. The original terms were four TotalFina shares for every three Elf shares.
TotalFina has revised upwards its estimate of cost-savings from 1.2bn euros to 1.5bn euros (pounds 970m). The merger will result in 4,000 job losses among a combined workforce of 130,000.
Thierry Demarest, the TotalFina chairman, will chair the enlarged company, which will have nine directors from Elf, nine from TotalFina and four representing the Belgian shareholders on the TotalFina board.
Mr Demarest said he would be open to other possible deals, depending on timing and conditions, fuelling speculation that ENI of Italy, continental Europe's biggest oil group, may join the enlarged French group. TotalFina is itself the product of Total's $12bn all-share takeover of Fina of Belgium earlier this year.
The Elf counter-bid had envisaged demerging the combined group's oil and chemicals operations, a move which Elf claimed would help generate total savings of 2.5bn euros. This will not now happen, although the two companies said that a joint study group would be set up to examine changes in the way their chemicals businesses were organised.
The combined group will have 18,500 petrol stations, mostly in Europe, refining capacity of 2.5 million barrels a day and total sales of 67bn euros.Reuse content