The pair was arrested in the southern city of Warri, an oil hub, on Wednesday, Delta state police spokesman Andrew Aniamaka said on Thursday.
The Foreign and Commonwealth Office (FCO) confirmed on Monday that Alanna Carson, David Donovan and Shirley Donovan had returned safely to the UK after their ordeal but a fourth Briton had died while being held in captivity.
Local media cited an unconfirmed report that 57-year-old Ian Squire from Shepperton in Surrey died after suffering from an asthma attack.
In a statement released by the FCO, his family said: "We are all deeply saddened by the loss of Ian, a loving father, husband, and devout Christian, who dedicated much of his life in the service of others.
"It's clear that Ian had touched many hearts with his kindness and grace."
The four missionaries were working for a Cambridge-based Christian charity providing free medical services to communities in rural areas around the Niger Delta creeks.
Kidnappings for ransom occur frequently in Nigeria; militants in the Niger Delta region and members of the Islamist group Boko Haram in north-eastern Nigeria have conducted several high-profile abductions.