McElduff’s conduct had been under the spotlight after posting a controversial video on Twitter on the anniversary of the Kingsmills massacre.
Sinn Fein supsended him last week for three months on full pay.
But relatives of those murdered by the IRA at Kingsmills said the punishment didn’t go far enough and called for him to resign.
Michelle O’Neill said Mr McElduff had been a “formidable” public representative for the past 20 years saying he recognised the controversy from his tweet and his continuing role in public office was compounding the distress to the victims of Kingsmills.
Mr McElduff said he did not want to be a “barrier” to reconciliation and healing.
Kingsmilsl survivor Alan Black welcomed the resignation.
“This past week has been truly awful for me. I am just hanging by a thread. But I am glad he has done the right thing,” he said.
In a stateement today, McElduff said: “It is with great sadness that, after more than 30 years as an active Sinn Fein member and public representative I am tendering my resignation as MP for West Tyrone.
“The reason I am doing so is because of the consequences of the Twitter video which has caused such controversy over the last week.
“But the deep and unnecessary hurt this video caused the families of the victims of Kingsmills is my greatest regret.
“I again offer my profound apology to those families and to the wider victims community.
“Had I been conscious of the connection to the terrible atrocity at Kingsmills I would certainly not have posted that tweet. I genuinely did not make that connection, not for a second did I make that connection in my mind.”
His resignation comes after he he posted a video posing with a Kingsmill loaf on his head on the anniversary of the 1976 massacre.
He added: “Kingsmilsl was wrong, unjustifiable and sectarian. It should never have happened.
“There was no intended reference to Kingsmills in my tweet. But I do accept that there are many people who do not believe this to be the case.
“I accept also that this view of what happened is deeply damaging to the reconciliation process that is so important to consolidating the peace process and to healing the pain and hurt of the past.
“I cannot undo the pain caused but I know that my continuing role as MP for West Tyrone will compound that sense of hurt and impede any reconciliation process.
“I wish to wholeheartedly thank my family and friends for their steadfast personal support during this difficult time, and the people of West Tyrone whom I have had the privilege to serve as their public representative for over 20 years. I have a deep gra for my native county and its people.
“I am an Irish republican and believe whole heartedly in the reunification of our country and an agreed Ireland in which we heal the wounds of the past together.
“Reconciliation is essential, but that message is not being heard at this time.
“I do not wish to be a barrier to reconciliation and healing and in that spirit I again offer my sincere apologies to the survivors and families of those murdered at Kingsmills.”
Responding, Sinn Fein Northern Ireland leader Michelle O’Neill said: “Yesterday evening, Barry McElduff informed me of his intention to resign as Sinn Fein MP for West Tyrone.
“Barry is doing so as a consequence of the unintended hurt caused to the Kingsmills victims and their loved ones by his recent social media tweet.
“Barry recognises that this controversy and his continuing role in public office is compounding the distress to the victims of Kingsmill, and again offers his profound apology to those families and to the wider victims community.
“He has said that he does not want to be a barrier to reconciliation and I respect that decision.
“Barry has served Sinn Fein and been a formidable champion for the people of West Tyrone at local government, Assembly and Westminster level over the past 20 years and has done so with great commitment, energy and determination.
“For this I want to personally thank Barry and his family, Paula, Niamh, Blannid and Patrick.
“Over the coming weeks Sinn Féin will focus our full efforts on the restoration of the power-sharing institutions on the basis of equality, integrity and respect and fulfil the mandate we received from the electorate in two successive elections last year.”