Security sources had said that the abduction was carried out as the Briton was travelling from the airport in Lagos' Ikeja neighbourhood towards the city centre.
His driver was reported to have been shot and injured in the attack.
Police tracked the suspects by the phone number used to make a $1m ransom demand from the victim's family.
The British national was held in an unfinished two-storey building in the Okota Isolo area of Lagos state.
One suspect has been arrested.
Kidnappings of both foreigners and wealthy Nigerians for ransom are fairly common in parts of the country.