A Derry board statement said Barton had been appointed in September 2015 "for an agreed period of two years".
"We would like to sincerely thank Damian, his management and all players who have represented their county during this period," it read.
The statement added that nominations for the job would be sought from clubs.
Barton had a creditable first year in charge of Derry as his side reached the Dr McKenna Cup Final and also narrowly missed out on qualifying for the All-Ireland quarter-finals after losing by a point to eventual semi-finalists Tipperary in the last qualifying round.
However despite that promising opening season, Barton's squad was badly depleted this year by the withdrawal of several experienced campaigners.
The under-strength Oak Leafers suffered relegation to Division Three of the Football League on points difference and then were well beaten by Tyrone in their opening Ulster SFC game for the second successive season.
While they regrouped to beat Waterford in the qualifiers, Saturday's extra-time defeat by Mayo saw Derry exiting from the championship.
Barton side were leading the Castlebar game up until a minute from the end of normal time but despite a brave effort, Derry had nothing left in extra time as Mayo eventually won 2-21 to 1-13.

He wants to transfer the remaining 91 detainees to their home countries or to US military or civilian prisons.
But Congress is deeply opposed to terror suspects being held on US soil and is expected to block the move.
The prison costs $445m (£316m) to run annually and closing it was a 2009 promise from President Barack Obama.
Human rights campaigners have repeatedly complained about the prison in Cuba, which has held 780 detainees since it opened in 2002.
The president told reporters on Tuesday it undermined national security.
"This is about closing a chapter in our history," said Mr Obama. "It reflects the lessons we've learned since 9/11 - lessons that must guide our nation going forward."
But Republican presidential candidate Marco Rubio was scathing in his criticism, saying Guantanamo prisoners do not belong on US soil.
"These are literally enemy combatants," he said, adding he would ship terrorists straight to Guantanamo "to find out what they know".
Life after Guantanamo prison
Will Guantanamo prison finally close?
There are four main components in the White House plan:
It estimates the move would save up to $180m (£128m) a year in cost savings.
The president, who will complete his second and final term in January, said it was important not to pass the problem on to his successor.
"Keeping this facility open is contrary to our values. It undermines our standing in the world. It is viewed as a stain on our broader record of upholding the highest standards of rule of law.''
President Obama has tried for years to close Guantanamo. He and his deputies say that it hurts the reputation of the US and that militants use "the infamous orange jumpsuit", as one senior administration official described it, as a recruiting tool.
But members of Congress have baulked at Mr Obama's plan to close the prison, saying they believe it should remain open - and they don't want any detainees to be transferred to the US. Representative Mike Pompeo of Kansas, for example, said the prisoners should "stay right where they are".
Lately, though, White House officials said that lawmakers, or at least some of them, seem more receptive to the idea.
A senior administration official told reporters that there's "room for conversation". That's important since Mr Obama has less than a year to close the prison - and for him time is of the essence.
Guantanamo Bay is located on an American naval base in south eastern Cuba. Former US President George W Bush opened it to accommodate foreign terror suspects after the 9/11 attacks on the US.
One of the key complaints from human rights groups is that many detainees have been held there without charge or trial.
White House officials said they could not give any names of people being held, but the New York Times has its own list.
The Obama plan does not specify where in the US detainees would go.
But the Pentagon has considered 13 different locations in the US, including seven prisons in Colorado, South Carolina and Kansas, and six other places on military bases.
Damian Barton's reign as Derry football manager appears to be over after the county's GAA board asked for nominations for the post.
[NEXT_CONCEPT]
The White House has presented to Congress a plan to close the Guantanamo Bay detention facility, one of the president's long-standing goals.