The politician has made the decision to step down with immediate effect over a £6,750 payment he received back in 2010 from PR company Weber Shandwick without declaring it.
Mr McDevitt had been the managing director of the company, but quit to move into politics and was chosen to succeed the SDLP's Carmel Hanna in 2010.
Fighting back tears, Mr McDevitt said that stepping aside was the "most honourable thing to do".
He told UTV: "I feel like I've let myself down, I've let my constituents down ..."
Mr McDevitt added that he had not been pushed by his party to resign and said he had taken the decision himself over what he called "a serious breach of the MLA code".
I have failed in my duty to uphold the standards expected in public office.
Conall McDevitt, speaking to UTV
Explaining what had happened, he said: "I provided support and mentoring to the new management team following my departure from the company (Weber Shandwick).
"I was never asked to nor did I ever represent any of the company's clients whilst an MLA."
The resignation comes after recent revelations that a company owned by Mr McDevitt's wife Joanne Murphy had received thousands of pounds over the past two years for research supporting him in his roles in the Northern Ireland Assembly and the Policing Board.
It emerged that JM Consulting was listed in Mr McDevitt's expenses, but that it was not initially declared as being his wife's company.
Mr McDevitt had denied doing anything wrong and said that his wife had not benefitted financially.
The company which she owned received money to pay researchers £16,000 for work on issues pertaining to the Policing Board, and a further £14,000 for Assembly-related issues.
It is understood that Joanne Murphy, who has a Phd in police reform, only carried out research relating to the Policing Board.
The payment made to Mr McDevitt by Weber Shandwick was also made through JM Consulting.
Conall McDevitt has done the right thing by resigning ... I welcome Conall’s speedy and definitive response in this regard and accept his resignation.
Alasdair McDonnell, SDLP leader
"My failure to register these interests at the time means that I have fallen below the standards of expected of me in public office," Mr McDevitt said.
"I have done my best to discharge my duties as an MLA with integrity, but there is no question that I failed to do so on this occasion.
"I apologise unreservedly for my failures in this regard."
Born in Dublin, Mr McDevitt was formerly the director of communications for the SDLP and served as a special adviser in the first power-sharing executive in Northern Ireland.
As well as being a member of the Policing Board, he was a party spokesman on health issues and sat on the Stormont Health Committee.
Mr McDevitt launched a leadership bid in 2011, but lost out to Alasdair McDonnell.
On Wednesday evening, Mr McDonnell said his party colleague had "done the right thing by resigning."
"Conall will be a loss to the Assembly party and to South Belfast and I would like to wish him and his family all the best for the future," he added.
Sinn Féin's deputy First Minister Martin McGuinness tweeted: "Conall McDevitt's resignation from politics today is sad for him and his family. I wish them all the best in the future."
TUV leader Jim Allister commented on Twitter: "Though opposed to Conall McDevitt's politics, he had talent and ability well above the average MLA. Not an easy decision for him".