Shaikh Abdur Rahman, 50, leader of the banned Jumatul Mujahedeen Bangladesh, gave himself up in Sylhet city, 190km northeast of the national capital Dhaka, early on Thursday, Faisal Alam, the area's government administrator, said.
His organisation has been blamed for bombings across Bangladesh in recent months that killed 26 people and wounded dozens.
More than 500 security forces took part in a 30-hour siege on Rahman's hideout in the northeastern city, Alam said.
Two of Rahman's aides, who were also holed up in the single-storey house in the city's Shaplabagh residential district, also gave themselves up.
Security forces took them to the office of Rapid Action Battalion, an anti-crime force that carried out the operation since early Wednesday.
Abdul Aziz Sarkar, a senior security official overseeing the operation, said: "We are so glad that we have been able to get him [Rahman] alive. It has been a great achievement."
Some groups want Islamic rule to
replace existing secular laws
Security agents discovered four home-made bombs in Rahman's hideout, Sarkar said.
On Wednesday security forces detained nine people after firing tear gas into the hideout. They included Rahman's wife, four grown children and a daughter-in-law, officials said.
They said three children who were with their parents were also taken into custody but were not considered suspects.
Rahman, who studied in a university in Saudi Arabia in the 1980s, founded his group in 1998. It has been campaigning to introduce Islamic rule in Muslim-majority Bangladesh, which is governed by secular laws.
Rahman and Siddiqul Islam, his deputy, who is also known as Bangla Bhai, are the South Asian nation's most wanted fugitives.
A court in southern Barisal city sentenced both in absentia to life in prison last month for ordering a bomb attack that killed two judges in a neighbouring town last year.
Authorities have offered rewards for their capture and distributed posters with pictures of the two in different guises all over the country.
The pair are also wanted in several other bombings across Bangladesh last year, including a string of blasts on 17 August that killed two people and injured 125 and attacks on courts that killed 24 more people, including lawyers and policemen.