The agreement is subject to approval by the financial regulator. Investec Ireland is owned by South African bank Investec.
Quinn Financial Services Group has a 25% stake in NCB. There are around 60 other shareholders, mainly staff.
NCB was originally founded by Dermot Desmond in the 1980s. It currently employs 120 people and has around €1.3 billion of private client funds under management.
"The NCB business will complement our successful capital markets business in Ireland and is consistent with the group's overall objective to expand its fee-based and capital light activities," said Michael Cullen, CEO of Investec Ireland.
"The deal will bring together two like-minded and innovative businesses whose operations are very complementary and whose combined experience and expertise will create real added value," said NCB CEO Conor O'Kelly.
