It means they can now serve in areas such as the United States, Canada and Australia.
Pope Francis gave his approval in what's been described as a bid to enable this branch of the Church to continue.
Eastern Catholic churches follow a different theology to the traditional Roman Catholic teachings. More common across the Middle East there are small numbers of groups who worship in the west.
In areas across the Middle East, the Church has been able to ordain married men as the Vatican allows them to maintain their own properly constituted discipline on the issue of celibacy.
However, up until now Eastern churches in the West were banned from appointing married priests.
In recent years it's claimed some had been appointed without Vatican approval.
Some commentators have suggested this could be the first step to seeing the wider Catholic Church changing law to allow priests to marry.