Mr Nechama, who had been a member of the board for a decade, will be replaced by Dan Danker, although no date has been set for him to commence his new role.
The resignation comes after Mr Nechama recently sold his share in the company's majority shareholder, Arison.
Meanwhile, the bank also announced that, after long service as a director, Izit Izakson will be promoted to the deputy chairwoman.
Both of the new appointments will need to be approved by the Israeli regulatory authorities.
Earlier this week, a subsidiary of the bank Hapoalim Switzerland, which has a presence in Moscow, Hong Kong and in Europe, confirmed that it is to expand into Singapore.
News of the changes in the boardroom come in the week that Bank Hapoalim declared it is to sell 25 per cent of credit card company Isracard to Israel Phoenix Assurance.
Hapoalim is the largest bank in Israel.