Born in Ghana, Mr Annan held the post for nine years between 1997 and 2006. He was awarded the Nobel Peace Prize in 2001.
The diplomat was invited by ex-Deputy Prime Minister Lord Prescott and is due to deliver a lecture at Hull City Hall in September during the annual Freedom Festival.
Lord Prescott said: "I am looking forward to welcoming Mr Annan to Hull."
He added: "His experience with children and young people in conflict areas is world renowned and he will be able to give a valuable insight into his experiences."
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Mr Annan is to give a speech at the Wilberforce Lecture, which celebrates the work of Hull-born abolitionist William Wilberforce, who lobbied to ban the slave trade and introduced anti-slavery motions in parliament.
Councillor Andy Dorton, chair of the Wilberforce Lecture Trust, said: "Mr Annan is a prominent figure and the Kofi Annan Foundation seeks to mobilise political will to overcome threats to peace, development and human rights.
"His experience in this important global issue and the messages Mr Annan will share at the lecture will no doubt resonate strongly with the purpose of the Wilberforce Lecture Trust and what we are trying to accomplish."
Previous high-profile speakers include Archbishop Desmond Tutu, Archbishop John Sentamu and Nigerian playwright and poet Wole Soyinka, who won the Novel Prize for Literature in 1986.
Former United Nations Secretary-General Kofi Annan is to visit Hull.