Martin succeeds Jim Shaw, who has held the post since November 2010, following his election on Tuesday evening.
He has previously held the positions of Deputy President, Vice President and Treasurer of the organisation.
"I am honoured to have been elected and look forward to serving the football community across NI," said Martin.
"It has been a remarkable few weeks for the international team in France and my aim will be to help the Association build on that success and to help grow the game at all levels," he added.
Linfield FC board member Jack Grundie was elected to the role of first Deputy President at the meeting, with Crawford Wilson, former President of the County Antrim FA, was elected as the second Deputy President.
Martin was voted in as one of the IFA's deputy presidents in 2013, having failed to be voted into the position in 2011 after failing a suitability assessment.
That aspect of the criteria for occupying senior office in the organisation has since been removed.
Martin initially resigned in the wake of the sacking of former chief executive Howard Wells in 2010 but returned to the Association on the back of a unanimous vote at a meeting of the IFA Council three years ago.
Wells' dismissal cost the association £500,000 in an unfair dismissal case and both Martin and former president Raymond Kennedy were subsequently removed from their positions under pressure from the then Sports Minister Nelson McCausland, who deemed the organisation not fit for purpose.
David Martin has been elected as the new president of the Irish Football Association at a meeting of the organisation's Council at Windsor Park.