The county voted "no" to a Welsh Assembly in 1997, but Wales voted "yes", and two years later the Cardiff-based body came into being.
Many Flintshire people associate themselves more with North West England than with South Wales, but Mr Murphy, h
imself an early opponent of devolution, claims the county has "come around" to the Assembly.
Speaking at the Airbus plant in Broughton during a visit on Wednesday, he said: "It does take time for new institutions to bed in but the Assembly is an established part of Welsh life and it's not going to go away now.
"People have grown used to it and we have to make sure it works now."
Mr Murphy added that, as a border county it is also a long way from Cardiff, it was inevitable that Flintshire may take longer to accept the Assembly than other areas.
It may not have been easy over the last decade, but people who were unsure about the Assembly have now come to accept it as "part of the national landscape of Wales", he said.
Mr Murphy's comments echo those of the Assembly's first minister, Rhodri Morgann made during a visit to the region last year, in which he claimed the Assembly has "won Flintshire over".
In an interview with the Leader, Mr Morgan said: "There is a preposition that Cardiff is a long way away and the orientation of people who live in this area is such that when they think of capital cities they think of Manchester and Liverpool.
"For complex hospital treatments they look to Christies in Manchester and Alder Hey in Liverpool, or for holidays they think of John Lennon or Manchester airports.
"So the tie between North East Wales and North West England is very strong and we have to recognise that – even in terms of football teams people support, Everton, Manchester United and Liverpool – it's a fact of life.
"Airbus is the best example of that, with 38 per cent of its workforce living in England."
But Mr Morgan claimed the north-south divide does not exist in Wales in terms of identifying more with Wales or England, but rather there is an east-west split.
He said: "What showed up in the referendum was an east-west split not a north-south split."
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