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 3,695 migrants have drowned this year or remain missing.
The symbolic milestone was passed on Monday, the IOM said, with the total for land and sea reaching 1,005,504.
The figure covers entries via six European Union nations - Greece, Bulgaria, Italy, Spain, Malta and Cyprus.
Half of the refugees crossing the Mediterranean were from Syria, 20% were from Afghanistan and 7% from Iraq, the IOM says.
Most of the migrants who died - 2,889 - were making the sea crossing between north Africa and Italy, while more than 700 died in the Aegean crossing to Greece from Turkey.
Only 3.5% of migrants made a land journey to Greece or Bulgaria via Turkey. The IOM gathers its statistics from registrations, law enforcement agencies and its own monitors. But IOM director general William Lacy Swing said it was not enough to just count the figures.
He said: "We must also act. Migration must be legal, safe and secure for all - both for the migrants themselves and the countries that will become their new home."
A joint IOM and UNHCR statement said "a more co-ordinated European response is beginning to take shape".
However, it said more needed to be done to improve reception facilities, accommodation, registration and to identify those who do and do not qualify for refugee protection.
The huge influx of migrants has caused significant political rifts within the EU. Some states have put up fences and introduced border controls despite the EU's border-free Schengen area.
The EU last week agreed to increase the numbers of Frontex border agency staff in Greece, a key arrival point. Once they arrive in Greece, many migrants then try to travel north via the Balkan states, many heading for Germany and the Nordic countries.
Germany alone has received a million refugees and migrants this year, although many were already within Europe. Macedonia is now refusing to allow anyone through its Greek border who does not come from a war zone.
A UN report last week warned that the number of forcibly displaced people worldwide would "far surpass" 60 million this year.
