The evolutionary scientist, whose books include The God Delusion, said Wales was "ahead of the rest of the UK" in showing a decline in religious belief.
The census found 32% in Wales have no religion, against a UK figure of 25%.
The Church in Wales said Christianity was "no longer the default setting" for many, but the picture was complex.
Of those in Wales who described themselves as believers, the number of Christians fell by 14 percentage points to 57%.
Prof Dawkins said: "I congratulate the people of Wales in coming out ahead of the rest of the United Kingdom in this respect - well done."
He told BBC Radio Wales' Good Morning Wales that he believed in the "wonder" of scientific truth.
He said: "People who are educated in religion are positively encouraged not to investigate, not to think sceptically about why they are here, but instead to accept what people wrote 2,000 years ago.
"I guess we do need focal points for communities but you can say also that religion has been a focal point for all sorts of backward, indeed bigoted, thinking about homosexuality, about abortion, the right to die, that we're seeing at the moment."
He added that research commissioned by his foundation meant that the outlook for Christianity in the UK was "even more pessimistic" than the census data suggested.
He said many of those who put themselves down at Christian did so because they thought of themselves "as a good person" rather than due to belief in the virgin birth, or of Jesus Christ as the son of God.
Prof Dawkins dismissed the figures for people saying they were a Jedi knight or that heavy metal music was their religion as "a kind of protest" against the inclusion of a census question on religion.
The census found those in Wales who are Muslim was 1.5%, up from 0.7% in 2001, while there were also slight increases Hindus or Buddhists, both up from 0.2% to 0.3%.
There was also a rise in people saying they had other faiths, from 0.2% to 0.4% while the percentage who said they were Sikh or Jewish remained unchanged between 2001 and 2011 at 0.1%.
Churches said they were not discouraged by the findings, and argued that Christian belief was still clearly alive and well.
Following the census results, the Church in Wales said: "It should also be borne in mind that statistics can't show the whole picture in matters of faith.
"The past few months, for example, have seen people in different parts of Wales turn to churches in their thousands following various tragic events: in Machynlleth, in Ely, in St Asaph.
"People find God when life gets tough and it is the church's privilege to be there for them whenever and wherever we may be needed."
Atheist author Prof Richard Dawkins has congratulated the people of Wales after nearly a third of them revealed in the 2011 census that they have no religion.