All of them were detained in Pabna on Monday, ACC spokesperson Pranab Kumar Bhattacharya told bdnews24.com.
Most of them hail from Sirajganj's Belkuchi Upazila.
The 19 constables are Ayub Ali, Kamrul Islam, Abdul Kuddus Sheikh, Ali Abbas, Md Ali, Sabuj Mia, Abu Hanif, Saiful Islam (1), Md Ferdous, Saiful Islam (2), Haider Ali, Md Buddhi Mia, Suman Kumar Sarker, Shahidul Islam, Abdul Awal, Amirul Islam, Al Amin, Sohel Rana and Suman Ahmed.
The national anti-graft agency in a media statement said their Pabna Office Deputy Director Abu Bakar Siddique and Deputy Assistant Director Abul Kalam made the arrests.
The 19 were presented before a court on Monday afternoon, said bdnews24.com's Pabna correspondent.
They were arrested in a case filed by police on Nov 4, 2014, at Sirajganj Sadar Police Station, Bhattacharya said.
He said these 19 people had managed to get job as constables in the freedom-fighter quota using the fake certificates. But their recruitment process was suspended after the case was started.
Abu Bakar Siddique said later the case was transferred to the ACC.
The accused were brought in for questioning and arrested after preliminary investigations found proof of the charges levelled against them, he said.
Source: Bangladesh's First Internet Newspaper