The 70 per cent stake will cost Nigeria's Guaranty Trust Bank (GT Bank) $100 million.
Fina Bank has total assets of $338 million with operations in Kenya, Rwanda and Uganda, a GT Bank statement said, adding that its agreement to acquire the privately-held Kenyan bank is subject to regulatory approvals.
"GT Bank will enter East Africa through a multi-country and scalable platform, thus expanding its international presence in Sub-Saharan Africa," the Nigerian lender said.
Shares in GT Bank which has gained 13 percent since the start of the year, inched up 1.66 percent to 26.40 naira per share on Thursday, valuing the lender at around $5 billion.
The top-tier bank said it will acquire the majority stake in Fina Bank, set up in 1991, through a share purchase from current shareholders and direct investment.
Chief executive Segun Agbaje has said GT Bank was eyeing expansion opportunities in East Africa after building out operations in West Africa to tap into the regions fast growing economies and ease of doing business.
Fina Bank has $184 million loan book as at 31 March, 2013 and operates from 38 branches across three East African nations.