The laws propose two fairs a year -- in March and September -- rather than every month.
Traders will have to register with Dublin City Council, giving their PPS number and paying a fee of €10 for each horse.
The local authority will set up a marketing group of horse owners, business representatives and Smithfield residents to promote the market.
Horse owners have asked that the €10 fee not be increased for five years and that online registering be made available.
They have also requested a provision to allow for a one-off fair on special occasions.
Fine Gael councillor Gerry Breen, the chair of the casual trading subgroup that drew up the laws, praised the horse owners for the "positive and realistic way they negotiated".
"We now have a job of work to do to make the March Smithfield fair a fantastic success."
The bye-laws were drawn up after violence at the Dublin 7 event in March last year, leading to demands for stricter controls.
Since March last year, a significant amount of resources have been spent by gardai, the council, Revenue Commissioners and other State bodies.
The Draft Smithfield Horse Fair bye-laws stipulate the event would be "solely for the sale of horses".
Traders would also be prevented from entering the market unless they produced a valid equine passport, as well as public liability insurance for the display or selling of the animals in a public place.