Gmail's unique selling point when it was launched in 2004 was masses of free storage space, currently 2.8 gigabytes.
Its trial service in the UK and elsewhere has run for more than two years, allowing rivals Hotmail and Yahoo to catch up.
Google now also offers downloadable software for mobiles, which makes it easy to read emails on the go.
Known as Gmail in most countries, it had to change its name to Google Mail in the UK and Germany due to trademark disputes.
A by-product of moving from the invitation only system should bring to an end a current spate of people making money by selling Gmail addresses.
Gmail was already freely available in US and a few other countries.
Users can now freely sign up to Gmail in across Europe, the Middle East and Africa, as well as in Brazil, Australia, Russia and Japan.
Applications to use Gmail on mobile phones are now available in the UK, Germany and the United States.