The law scraps one traditional system that deemed South Koreans one year old at birth, counting time in the womb.
Another counted everyone as ageing by a year every first day of January instead of on their birthdays.
The switch to age-counting based on birth date took effect on Wednesday.
President Yoon Suk Yeol pushed strongly for the change when he ran for office last year. The traditional age-counting methods created "unnecessary social and economic costs", he said.
For instance, disputes have arisen over insurance pay-outs and determining eligibility for government assistance programmes.
Previously, the most widely used calculation method in Korea was the centuries-old "Korean age" system, in which a person turns one at birth and gains a year on 1 January. This means a baby born on 31 December will be two years old the next day.
A separate "counting age" system, that was also traditionally used in the country, considers a person zero at birth and adds a year on 1 January.
This means that, for example, as of 28 June 2023, a person born on 29 June 2003 is 19 under the international system, 20 under the "counting age" system and 21 under the "Korean age" system.
Lawmakers voted to scrap the traditional counting methods last December.
Despite the move, many existing statutes that count a person's age based on the "counting age" calendar year system will remain. For example, South Koreans can buy cigarettes and alcohol from the year - not the day - they turn 19.
Three in four South Koreans were also in favour of the standardisation, according to a poll by local firm Hankook Research in January 2022.
Some, like Jeongsuk Woo, hope the change will help break down Korea's hierarchical culture.
"There is a subconscious layer of ageism in people's behaviour. This is evident even in the complex language system based on age... I hope the abolition of 'Korean age' system and the adaptation of the international standard get rid of old relics of the past," said the 28-year-old content creator.
Another resident Hyun Jeong Byun said: "I love it, because now I'm two years younger. My birthday is in December, so I always felt like this Korean age system is making me socially older than what I actually am.
"Now that Korea is following the global standard, I no longer have to explain my 'Korean age' when I go abroad."
The 31-year-old doctor said South Korea's medical sector has already been adopting the international age system.
The traditional age-counting methods were also used by other East Asian countries, but most have dropped it.
Japan adopted the international standard in 1950 while North Korea followed suit in the 1980s.