The decision by the people of Wales means that the National Assembly will be able to pass laws in devolved areas without first seeking the approval of the UK Government or Parliament.
The new legislative powers will speed up the legislative process and make it more efficient, enabling the National Assembly to deliver better results for Wales.
First Minister of Wales Carwyn Jones said:
"I am very pleased that the people of Wales have voted in favour of the Assembly having greater law-making powers
"After more than a decade of devolution, we will for the first time now be able to legislate more effectively for the people of Wales, in Wales.
"The system we have used so far, under the Government of Wales Act, had an element of duplication, and created confusion about who was responsible for what. Removing that duplication will enable us to use our legislative capacity more effectively, and people will gain a clearer understanding of the role and responsibilities of the devolved institutions in Wales."
Deputy First Minister of Wales Ieuan Wyn Jones said:
"This vote represents a historic day for Wales that will provide the Welsh people with full law-making powers for the first time.
"I am also very proud that this referendum has marked the success of one of this Assembly Government's key One Wales commitments. This is a truly significant achievement that will resonate in this country every time legislation is needed. The people of our nation have voted for a more efficient and more effective legislature here in Wales, and future generations will benefit from their actions."
Assembly Government officials will now begin the task of introducing the relevant legislation so that the Assembly is able to use its newly acquired further-law making powers as soon as possible. This is expected to be from the start of the new Assembly in May.