The decisive 34-7 vote is a dramatic about-turn for an area that voted narrowly against the Assembly back in 1997 and campaigners believe it sends a powerful signal that the Assembly is ready for an enhanced role.
The vote, which attracted cross-party support and among the many independent councillors in Wrexham, was a symbolic milestone according to the councillor who submitted the motion.
Councillor Marc Jones, Plaid Cymru's group leader on the council, said:
"In a little over 13 weeks, Wales will have a referendum on whether the Assembly should have law-making powers in the 20 devolved areas it already makes decisions about, including health, education and housing.
"At the moment, any laws made in Wales have to be scrutinised and approved of by both the House of Commons and House of Lords in London. This has led to delays of up to a year in approving some important legislation, so a 'yes' vote will speed up the democratic process and do away with the current cumbersome process."
"The referendum on March 3 is about making the Assembly work better for all communities in Wales - including ours. At the moment the Assembly operates like a boxer with one arm tied behind its back. Gaining the power to make laws without a Westminster veto will speed up decision making in wales.
"A yes vote has no cost implications for the council or at a national level. If won, it says we are maturing as a nation and able to take a step forward in enhancing our democracy.
"If lost, it says we are happy with the overly bureaucratic set up we currently have and it could have huge repercussions for Wales, especially at a time when we’re trying to defend services.
"It’s great to see Wrexham leading the way in supporting this move – we’re the first council in Wales to put forward such a proposal. I'm sure others will now want to pick up on this and I hope we'll see a snowball effect throughout the country."
The full motion reads:
"Wrexham Council supports full law-making powers within the devolved areas for the Welsh Assembly. This will speed up the democratic process in Wales and do away with the cumbersome process we currently have, for the benefit of both national and local government."