Delwar Hossain and his wife were charged with homicide in December.
The couple arrived at Dhaka magistrates court, and have now been jailed after their plea for bail was rejected.
Although arrests warrants had been issued in December, they had been living freely in Dhaka.
It was not clear why they decided to give themselves up.
They face a maximum sentence of life in prison if convicted.
The Tazreen fire was the country's deadliest garment factory fire, and brought attention to working conditions in the all-important garment industry.
The country suffered an even greater tragedy just months later when the Rana Plaza garment factory complex collapsed on the outskirts of Dhaka, killing 1,135 people.
Mr Hossain and his wife, Mahmuda Akter, are among 13 people who were charged over the fire.
An investigation found that when the blaze broke out, managers and security guards told workers it was part of a regular drill, and it was too late for many to escape.
Investigators said the nine-storey factory had no emergency exits, and workers desperately trying to leave found that some of the gates were locked from the outside.
Victims of the fire, many of them women who were paid as little as $37 ( £23) a month, found themselves overcome by the smoke inside the building.
The Tazreen factory produced clothing for big retailers including Wal-Mart,
This the first time Bangladesh has sought to prosecute factory owners in the influential garment industry, which is the world's second largest after China and a vital part of Bangladesh's economy.
Two owners of a Bangladesh garment factory where 112 workers died in a fire two years ago have turned themselves in to the authorities.