Procter & Gamble Co. is relocating its global skin, cosmetics and personal-care unit from its Cincinnati headquarters to Singapore, following a decision to base the business in the fast-growing Asia beauty market.

The move is significant symbolically for a centralized company that has been working to move employees and manufacturing facilities closer to its key customer bases. The change will take about two years and see some 20 people move to Singapore, P&G spokesman Paul Fox said.

The...