The largest individual award in the world, it comprises $5m over 10 years and $200,000 annually for life thereafter, and up to $200,000 a year for 10 years towards the winner's public interest activities and good causes.
The prize aims to encourage African leaders "who fully dedicate their tenure of office to surmount the development challenges of their countries, improving the livelihoods and welfare of their people and consolidating the foundation for sustainable development".
"The prize celebrates more than just good governance. It celebrates leadership," Annan said in a statement.
Ibrahim said: "As a man who has reconciled a divided nation and built the foundations for a stable, democratic and prosperous future for the country, [Chissano] is a role model not just for Africa, but for the rest of the world."
Chissano was selected by the prize committee of six eminent individuals who assessed every sub-Saharan African leader who had left office in the last three full calendar years on their exercise of leadership.
The committee drew on research from the recently published Ibrahim Index of African Governance, and a range of other sources, to assess the quality of governance in the areas of economic and social development, peace and security, human rights, democracy and the rule of law.
Annan said: "President Chissano's achievements in bringing peace, reconciliation, stable democracy and economic progress to his country greatly impressed the committee. So, too, did his decision to step down without seeking the third term the constitution allowed".
Praising Mozambique's economic progress, poverty reduction programmes, infrastructure development and work to tackle HIV/Aids, Annan said that "it is his role in leading Mozambique from conflict to peace and democracy that President Chissano has made his most outstanding contribution".