It clears the way for Franklin to become a Swan, provided Hawthorn are unwilling to match the deal.
The AFL has been investigating the deal since it was lodged by the Swans last week, to ensure it did not breach Sydney's salary cap or break any player movement rules.
The league demanded the Swans' board provided written guarantees on certain conditions that would be met before approving the deal.
They included a stipulation that the specific financial commitment for each year of the nine-season contract will count towards the Swans' salary cap, even if Franklin retires earlier.
The Swans' board will have to meet with the AFL each year to review how the club are managing their total player payment obligations in regard to the contract.
The AFL also gained assurances from the Swans that they had gained all information needed to properly assess a contract of that length, including medical reviews and long-term financial planning.
AFL general counsel Andrew Dillon said those guarantees had been needed given the unprecedented commitment of total player payment funds to a single player over such a long term.
The league also reiterated to the Swans that the 9.8 per cent cost-of-living allowance built into their salary cap, along with that of Greater Western Sydney, was under review and could be removed or varied from 2015 onwards.
Hawthorn have three days to decide whether they'll match the offer, in which case Franklin would have to either stay with the Hawks or put himself in the national or pre-season drafts.
But that is expected to be a formality, with Hawthorn having given no indication they will stand in the way of the two-time premiership star's desire to join the Swans.
Franklin had been widely expected to join the Giants, but shocked the wooden spooners by rebuffing their $7.2 million, six-year offer in favour of the Swans' nine-year, $10 million deal.
The 26-year-old will be 35 by the time his contract with the Swans is completed.
The ability of Sydney to fit him into their salary cap sparked a wave of fresh uproar from rivals over their cost-of-living allowance.
That allowance was already a subject of controversy after the Swans followed their 2012 premiership by recruiting star forward Kurt Tippett from Adelaide last off-season.