He was initially detained in September 2021 in connection with a conspiracy to smuggle 17 men, women and children in the UK in the back of a van, the NCA said in a statement.
It followed an operation in June 2019 which saw a British-registered Mercedes van intercepted by Dutch police, who were working with the NCA.
A group of Afghan migrants had been loaded on board near Breda in the Netherlands, and the vehicle was travelling towards the Hook of Holland to get a ferry to the UK when it was stopped.
Costache, who also uses the name Vasile Matei, is alleged to have worked with a number of other people to organise the attempt.
He was charged with conspiring to facilitate illegal immigration and granted bail.
He failed to turn up to a court hearing in Croydon in June this year so a warrant was issued for his arrest.
Last month Costache was found and detained by Romanian police in the town of Ploiesti, north of Bucharest, where he lived.
He was returned back to England on Monday and appeared before Westminster Magistrates on Tuesday.
He has been remanded in custody to appear before Croydon Crown Court on November 25.
NCA senior investigating officer Chris Hill said: “Through working with partners in Romania we were able to locate Costache and ensure his return to the UK to face the courts.”
Costache is one of 16 people due to stand trial in January 2023, following a wider NCA investigation into money laundering and organised immigration crime. Two other individuals have pleaded guilty.
It comes a week after two suspected people smugglers were arrested as part of an international crackdown on immigration crime.
The men are being questioned over facilitating small boats crossings.
Metropolitan Police detectives worked with immigration enforcement officers to arrest the London-based pair on behalf of Belgian authorities, the Home Office said.