The European Union flag has been lowered outside the National Assembly as Brexit formally takes effect.
The UK left the EU at 23:00 GMT, three-and-a-half years after the June 2016 referendum.
Earlier on Friday, First Minister Mark Drakeford said whatever "feelings we have in our heart", Wales was leaving the EU with "our heads held high".
On Saturday, about 40 people took part in a pro-EU rally in through the centre of Cardiff.
In a message released on social media an hour before the UK's departure, Prime Minister Boris Johnson vowed to "bring the country together" and "take us forward".
He said: "For many people this is an astonishing moment of hope, a moment they thought would never come.
"And there are many of course who feel a sense of anxiety and loss.
"And then of course there is a third group - perhaps the biggest - who had started to worry that the whole political wrangle would never come to an end.
"I understand all those feelings and our job as the government - my job - is to bring this country together now and take us forward."
Wales voted to leave the EU at the 2016 referendum by 52.5% to 47.5%.
Mr Drakeford, Welsh Labour leader as well as first minister, gave a speech in Cardiff on Wales' future relationship with Europe.
"Whatever the different feelings we have in our heart" on departing from the bloc, he said, "we do so here in Wales with our heads held high".
"Wales remains a European nation - we are citizens of the world as well as of Wales and at 11 o'clock today all of that will be not less but more important than ever."
Mr Drakeford also warned the prime minister that Wales and the Welsh Government would "not be hoodwinked by any simplistic assertion that Brexit is now over and done".
"We will not be browbeaten by the assertion that the decision to leave the European Union is a decision that brings an end to debate or to discussion," he said.
"We will not simply be bored into submission by the reality that Brexit is with us, not just for today but for years and years to come.
"Leaving the European Union brings stresses and strains in the United Kingdom as well," Mr Drakeford added.
"The Welsh Government will be there as we have been over recent years leading the call for serious attention to be given to the way in which the United Kingdom is to operate together in the aftermath of our membership of the European Union."
'Exciting and a relief'
Attending a party in Cardiff for Brexit Party assembly members and staff, Caroline Jones said Brexit was both "exciting and a relief".
"We can now all move on as Wales and as the UK," the party's AM for South Wales West said.
"We hope investors will now be attracted to our little country, Wales, because we are open for business to the rest of the world.
"We want unity, peace and stability because that's what we haven't had. We were in limbo for three-and-a-half years so it's exciting, and a relief in a lot of ways."
Sally Stephenson, the owner of a stationery shop in the Vale of Glamorgan, said her business was "utterly dependent on the single market".
"I think people think the single market is for big business like Airbus and Tata Steel but a small one like this on Cowbridge high street is really reliant on bringing stock in from the single market," she said.
"I import stock from France, Germany, Italy, Denmark, Romania - it comes from everywhere."
Meanwhile, Cardiff and Nantes published a joint letter reaffirming their "friendship and commitment to our twin city status," which dates back to 1964.
"Together we are citizens of Wales and France, and citizens of Europe," the letter read.
While the UK left the EU's political systems on Friday night, it now enters a transition period where the country sticks to European Union rules.
This runs to the end of 2020, during which time the UK government holds negotiations on a future trading relationship with the EU.
Welsh Secretary Simon Hart said: "Today marks a new chapter in our history as we finally deliver on the decision made by the Welsh people and leave the EU.
"We are leaving as one United Kingdom with a mission to build better infrastructure, make our streets safer, clean up our environment and make our union stronger."
On behalf of all European Commission staff at the Representation in the UK, both past and present, in its main London Office as well as in its Offices in Belfast, Cardiff and Edinburgh, we would like to take this opportunity to thank all our partners and friends 7/9— EC Office Wales (@EUCommWales) January 31, 2020
Plaid Cymru had been among the parties battling for Remain. Earlier this week party leader Adam Price vowed to make Brexit work for Wales "as best we can".
Mr Price said: "Wales will always be friends of Europe and nothing will change that."
"It has been a pleasure and a privilege working with you all."
Analysis by Felicity Evans, BBC Wales political editor
Even though Welsh life will continue without much change in the short term, it doesn't mean Brexit isn't a big long term shift.
Manufacturing and the rural economy are big sectors in Wales and any future trade deal with the EU (and other deals with countries like the United States) will have a big impact on them.
The Welsh Government is calling for a guarantee they will be able to feed into the UK negotiating strategy when devolved issues are at stake. So far, Downing St hasn't agreed.
Another potential flashpoint is the UK government's replacement scheme for EU aid money. UK ministers say the Shared Prosperity Fund will "reduce inequalities between communities".
What we don't yet know is how it will work and who will control how the money for Wales is spent. The Welsh Government is adamant it should be them - again the UK government hasn't yet agreed.
Brexit is now an historical fact, but the shape of things to come is still a bit blurry.