But Juan Carlos Hidalgo, Latin-American project co-ordinator at the Cato Institute, said that the law does not mark a significant change in policy.
"The Mexican authorities were not [chasing] small-scale drug users before, so this law just legalises the status quo. But certainly it is a signal that Mexico is sending to the world that [going after] small-scale drug users is counter-productive," he told Al Jazeera.
"As long as drug production remains illegal, we are going to see the drugs traffickers running a black market. I don't see how the new measure will help calm down the drug violence in Mexico."
The maximum amount of marijuana for "personal use" under the new law is five grams, while a person can carry up to a half gram of cocaine.
For other drugs, the limits are 50mg of heroin, 40mg for methamphetamine and 0.015mg for LSD.
Those stopped and found in possession of drugs under the new limits will be encouraged to seek treatment, but those caught for a third time will face a mandatory health programme.
Under the previous law, possession of any amount of drugs could lead to a jail sentence, but authorities rarely prosecuted addicts found carrying small amounts.
"We couldn't charge somebody who was in possession of a dose of a drug, there was no way ... because the person would claim they were an addict," Espino del Castillo said.
But police often sought bribes from those they suspected of carrying drugs, under the threat of a stiff prison sentence.
"The bad thing [with the previous law] was that it was left up to the discretion of the detective, and it could open the door to corruption or extortion,'' Espino del Castillo said.
Mexico has in recent months aimed to separate drug addicts and casual users from drugs traffickers.
The traffickers' battle with Mexican security forces has led to the deaths of at least 11,000 people since Felipe Calderon took office as president in late 2006.