Avijit Roy and Ananta Bijoy Das were hacked to death earlier this year.
According to police, British-Bangladeshi Touhidur Rahman planned the killings.
Touhidur Rahman, an IT expert, is said to have links with a banned militant outfit, Ansarullah Bangla Team (ABT).
Police say his arrest will provide evidence about a total of four killings of secular bloggers this year.
Touhidur Rahman was also the alleged financier of ABT, The Bangladesh Daily Star reported.
He and two others were detained last night in the Dhanmondi and Nilkhet areas of Dhaka.
Bangladesh is officially secular but critics say the government has not done enough to stop the attacks.
Last week police arrested two other suspected members of ABT over the killing of atheist blogger Niloy Neel.
Niloy Neel was hacked to death by a gang armed with machetes at his home in the capital Dhaka.
In March, another blogger, Washiqur Rahman, was hacked to death in Dhaka.
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