Mr Stock da Cunha was a director at London’s Lloyds Banking Group.
The move follows Saturday’s surprise resignation of the bank’s previous boss and two senior board members.
BES was split into a “good” and a “bad” bank in August as part of a 4.9bn euros ($6.6bn; £3.9bn) rescue plan.
Novo Banco, the “good bank” containing the healthy assets from BES, is currently run by the “resolution fund” – set up as part of the eurozone’s banking reforms and funded by Portugal’s financial institutions.
The bank will eventually be sold off, with the proceeds used to pay back the loan.
Set for sale
Portugal’s central bank, which orchestrated August’s rescue plan, saidMr Stock da Cunha had been “mandated to form and lead an experienced team” to prepare the bank to be sold.
Mr Stock da Cunha has almost 30 years experience in banking, most of which he spent at a senior level at Santander’s Portuguese operations.
He replaces Vitor Bento, who joined BES in mid-July. Mr Bento, alongside two fellow board members, resigned on Saturday.
The three said that they had decided to leave because “circumstances have changed” since they joined the bank.