In 1966, Lyndon Johnson issued a proclamation designating the third Sunday in June to honor fathers. Finally, in 1972, President Richard Nixon signed a law declaring that Father's Day be celebrated annually on the third Sunday in June. It has been an official, permanent national holiday ever since.
The date changes, yes! Father's Day always falls on the third Sunday in June-which means its actual date changes year to year. For instance, last year, it fell on June 20, and the year before that, it fell on June 21.
third Sunday of June
The third Sunday of June is celebrated as Father's Day in the US and while India follows it, many other countries including Portugal, Spain, Croatia, Italy etc celebrate Father's Day on March 19