The multibillion-dollar firm, which sells products in 70 countries around the world, has opted to move to Britain despite the chance it will leave the EU after the June referendum.
Moving to the UK will help the company maximise direct connections to its global operations through a UK base, it said in a statement.
The change comes after it sold a portion of its North American business to a private investment firm.
The 130-year-old company did not give any detail on investment or job creation in the UK, although it said it would cut around 2,500 positions worldwide.
Sheri McCoy, chief executive, said: "We are taking another important step forward in the execution of Avon's transformation plan.
"With the recent completion of the sale of the North American business, our commercial operations are now fully outside of the United States, allowing us to dramatically rethink our operating model.
"The actions we are taking today will bring our corporate and commercial businesses closer together, which will drive efficiencies, improve operational effectiveness and deliver significant cost savings."