The Japanese manufacturer had argued to the FIA that being left out of 2014 suppliers Mercedes, Renault and Ferrari's 'unfreeze' loophole was unfair.
F1's governing body originally believed Honda should have to stick to the strict February 28 homologation deadline, as it had been free to prepare its turbo V6 throughout last year and the forthcoming winter period while its 2015 rivals had been locked into the so-called 'freeze'.
But after high-level meetings between disgruntled Honda chiefs and the FIA in recent days, British broadcasters reported on Saturday that McLaren's new works supplier has won the day.
"There is a will to be fair and equitable and that is why there is a discussion," McLaren team boss Eric Boullier told Sky.
"I very much believe that we will come out with a fair solution," he said.
It emerges that the complex solution agreed between Honda and the FIA's Charlie Whiting will allow the manufacturer to do a limited amount of engine development during the 2015 season.
The allowed amount will depend on how many of the 32 development 'tokens' rivals Mercedes, Renault and Ferrari have used by the time of the first race.
"If the three 2014 manufacturers have (for example) eight, seven and five unused tokens respectively at the start of the season, then the new manufacturer will be allowed to use six during the season," said Whiting in a document seen by the BBC.
We reported earlier that Mercedes, having utterly dominated the 2014 season, may in fact enter the first few races of this year with all 32 tokens still in its pocket.
"It's a late (rule) change," works Renault team Red Bull's Adrian Newey told Sky, "and we are sorting out with Renault the best way to play it — it's not exactly clear."