The two children, aged three and six, are looking for at least $520,000 (£370,000) in damages, Lagos court papers quoted in the Nigerian media said.
This is supposed to compensate for the money that their father would have been expected to provide them with until he turned 70.
Their lawyer, Bolaji Ayorinde, told the British Broadcasting Corporation (BBC) that he has had a lot of inquiries from relatives of people who died in the building collapse about the possibility of taking action.
Joshua, referred to by his followers as a “prophet,” is one of Nigeria’s best-known evangelists and is popular across Africa.
He blamed the 2014 incident on a small plane which he said had been circling the building, which was a multi-storey guesthouse in a Lagos compound belonging to the Synagogue, Church Of All Nations. This was dismissed by the Lagos coroner.
Ayorinde said he was not concerned about taking on the popular preacher arguing that “the law treats everyone as equal.”