The number represents a fourfold rise on the total last year.
The vast majority crossed by sea, with more than 800,000 travelling from Turkey to Greece. Most are refugees from Syria, Iraq and Afghanistan.
The IOM says that 3,695 migrants are known to have drowned this year or remain missing.
Earlier, the UN said the number of people forcibly displaced worldwide in 2015 is on its way to surpassing a previous record of almost 60 million.