The move comes after the cosmetics giant sold its North American business to private-equity firm Cerberus.
Avon had 28,300 employees outside its sold-off North American operations at the end of December. It said Monday it will book a $60 million charge in the current quarter due to the layoffs.
The company said it expects to save $50 million this year from payroll cuts and the closure of open positions. Starting in 2017, it expects to save around $65 million to $70 million a year.
Avon will keep facilities in Suffern and Rye, New York, and remain incorporated in New York. Its stock will still trade on the New York Stock Exchange.