Saudi Arabia, birthplace of Islam, and other Gulf states such as the United Arab Emirates, Qatar, Oman, Kuwait, Yemen and Bahrain are observing the festival on Tuesday.
"It has been established according to Shariah (Islamic law) the citing of the new moon of Shawaal this evening Monday…and thus tomorrow Tuesday is the first day of the blessed Eid al-Fitr," said the Saudi official news agency SPA in a statement by the royal court.
In the lunar Muslim calendar, each month begins with the sighting of the new moon, depending on when and where the new crescent is visible. Months last 29 or 30 days.
Indonesia, home to the world's largest Muslim population, celebrates Eid al-Fitr on Tuesday as well. Malaysia and Singapore, with large Muslim communities, also announced the celebration for Tuesday.
The Eid festival already began for Libyans and Sunni Muslim Iraqis on Monday and is expected to begin either Tuesday or Wednesday for Shia Muslims there.
Iraqi street vendor: Sunnis there
and Libyans are first to celebrate
A leader of the Sunni Muslim community called for a week-long ceasefire to allow peaceful celebrations.
Adnan al-Dulaimi, head of Iraq's Sunni religious administration, in an Eid sermon, also asked "the occupation forces not to deal with Iraqis as terrorists. We are peaceful, apostles of peace and not evil".
Neighbouring Iran joins in on the Eid festivities on Tuesday.
In occupied Palestine, the festival begins on Tuesday as well.
Muslims in the USA will be informed Monday night there whether the crescent moon has been sighted for Eid to be celebrated either on Tuesday or Wednesday.
South African Muslims, numbering 2.5 million, join most of the rest of the world's Muslims on Tuesday in celebrating Eid.
Eid festivities will begin in Pakistan on Wednesday.
Eid al-Fitr is mostly spent visiting family and friends with special meals prepared for the celebrations. In upholding the act of charity which is emphasised during Ramadan, meals are prepared for distribution to the destitute as well.