The company said on its website that it was disappointed but instead would focus on its site at Preston New Road near Little Plumpton.
Campaigners who had opposed the fracking application said they were delighted but the drawn out process should never have carried on.
The firm had applied in 2014 to drill at the rural farmland site at Roseacre at the same time it bid for the Preston New road site but both were refused by Lancashire County Council.
It appealed and a six week planning inquiry was held in 2015 at Blackpool FC's Bloomfield Road stadium. That appeal allowed the Preston New Road project to go ahead but refused Roaseacre on the grounds that HGV trucks could not get to the site down the narrow country lanes without endangering other road users.
The then Secretary of State for Housing, Communities and Local Government, Sajid Javed, said he was minded to allow Cuadrilla to drill up to four wells and frack them at Roseacre if a suitable transport mitigation plan could be derived.
A second public planning inquiry was held at Bloomfield Road.
On February 12, 2019, the Secretary of State for Housing, Communities and Local Government James Brokenshire refused planning permission on traffic and highways grounds.
Laura Hughes, Commercial and Projects Director at Cuadrilla, said: “We have been pursuing planning permission at Roseacre Wood for some time and it was naturally disappointing to hear it had been refused on traffic grounds by the Government last month.
"We had worked hard on the application and we believed the site provided an excellent opportunity to explore for natural gas in Lancashire. However, we acknowledge the findings of the lengthy review process and will not be appealing against the decision.
“We continue operations at Preston New Road where we have had high quality, natural gas back to the surface following hydraulic fracturing between October and November last year. Our first results were encouraging and our central focus remains there.”
Cuadrilla said the site in Preston New Road is the most advanced shale gas exploration site in the UK with two horizontal wells drilled into the Bowland Shale and permission for up to four as part of current planning permission.
Fracking there is currently on hold at the moment as the company assesses the results of fracking that took place before Christmas. Those sessions resulted in more than 50 small earth tremors. However, the firm has moved equipment back on site ready to continue the exploration process.
Barbara Richardson for the Roseacre Awareness Group said: "Roseacre Awareness Group are delighted to hear this news.
"We have been saying for years that the traffic issues, relating to the Roseacre Wood site are insurmountable, a fact recognised by LCC and two independent Planning Inspectors and ultimately by the Secretary of State.
"However we should have never had to go through this stressful process. We have spent thousands of unpaid man hours, and tens of thousands of pounds, producing evidence to support our case which now all seems worthwhile but it has cost us much stress and anxiety.
"At last we can breathe a sigh of relief and know that our community is safe and no longer under threat from this insidious industry.
"We would like to thank everyone for all their hard work and support including those at Lancashire County Council, and all seven town and parish councils, who worked with us.
"However we will continue to raise awareness as there are many more communities still under threat most especially our friends at Preston New Road."
Jamie Peters, campaigner at Friends of the Earth, said: “Cuadrilla throwing in the towel at Roseacre is yet another sign that fracking is a dying industry. Fracking can’t be done without triggering earthquakes, it’s not wanted by the public and it’s high time that the government drops it altogether.”