The politician made the decision to step down with immediate effect after failing to declare a £6,750 payment he received in 2010 from PR company Weber Shandwick.
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 the South Belfast constituency in 2010.
In an emotional interview with UTV, he admitted: "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."
He said that stepping aside was the "most honourable thing to do".
"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".
The payment made to Mr McDevitt by Weber Shandwick was issued through JM Consulting, his wife Joanne Murphy's firm.
Questions had already been raised about payments the former spin doctor had made to his wife's consultancy company.
It had emerged that Ms Murphy 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. Her firm JM Consulting was listed in Mr McDevitt's expenses.
However, it was not initially declared as being his wife's business.
Mr McDevitt had denied doing anything wrong, saying 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 Ms Murphy, who has a PhD in police reform, only carried out research relating to the Policing Board.
Dublin born, Spanish reared, Conall McDevitt was seen as a rising star in the SDLP and tipped to be the next leader.
However, on Thursday afternoon, he tweeted: "Thanks everyone for your kind words and messages. Just want to make clear that I will not be returning to public life in the future."
His resignation has sent shock waves through local politics and attention is now turning to who will replace him at Parliament Buildings as SDLP MLA for south Belfast, - but also as part of the SDLP delegation in the forthcoming all-party Haass talks.
The talks are to begin later this month, chaired by US diplomat Richard Haass. It is hoped which they will address contentious issues such as parades, protests, emblems and dealing with the legacy of the Troubles.
The leading candidates for the vacant Assembly seat are believed to be city councillors Claire Hanna and Bernie Kelly and party adviser Fearghal McKinney. The party's south Belfast members will take the decision in about four weeks.
Meanwhile, the SDLP deputy leader Dolores Kelly has told UTV the resignation has stunned its members.
"Devastation," she said, describing her reaction.
"And that's not an overstatement, there is a lot of sadness and a great deal of shock over what has happened this last couple of days."
But others have been quick to point out the lack of support he received from within the party.
Political commentator Brian Feeney said: "If members are under attack normally the party does rally round and supports them and that was conspicuous by its absence.
While former Alliance deputy leader Seamus Close added: "Where were other SDLP members? I think it has been sad that not so many of them came quickly to the fore publicly to give support or succour to Conall McDevitt and that does pose questions."