The Tunisian Football Federation (FTF) confirmed on Wednesday that he will take over on 1 July.
Lemerre's contract ends on 30 June which means the Frenchman will be in charge for the next three matches of the qualifying campaign.
Tunisia suffered a shock 2-1 defeat to Burkina Faso in their opening qualifier for the 2010 World Cup and Africa Cup of Nations.
Coelho, 58, started his playing career with Portuguese club Ramaldese CF and later played for Benfica and French club Paris Saint Germain.
Most of his coaching career has been spent in Portugal where he led club sides Sporting Braga and Salgueiros Porto.
He has also coached Portugal (1997-2000), Morocco (2000-02) and South Korea (2003-04).
He will travel to Tunisia on 19 June to hold preliminary discussions with officials at the FTF.
He will give his first news conference in the new job in 23 June.
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