Former Ballon d’Or winner Weah, 51, played under Wenger at Monaco between 1988 and 1992, long before turning to politics.
The ex-AC Milan star recently won 61.5 per cent of the nation’s vote in Liberia’s presidential election – with his inauguration to be held on January 22.
However, Wenger has joked he will only be able to attend should the impose a stadium ban on him for his comments regarding referees in recent weeks.
The Frenchman, 68, served a four-match ban last January on misconduct charges – with another charge set to see him banned from the stadium.
Weah’s inauguration will be held between Arsenal’s Premier League clash with Crystal Palace on January 20 and the Carabao Cup semi-final with Chelsea on January 24.
On Weah, Wenger said: “When you look at his life, the life of this guy is a film. It is unbelievable. It is a fantastic film.
“I saw him in Monaco, looking lost, not knowing anybody, not being rated as a footballer.
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“Yet he became in 1995 the best player in the world and now he is president of his country. It is unbelievable.
“He was always strong mentally, convinced he has a mission.
“When he played at Monaco, it was during the time of war in Liberia and I saw how much he suffered with his country.
“The love for his country and his people, and the care he had for his people. Today when I look back, I have seen him crying when the war was on.
“But this is a happy story and I wish him a happy presidency. He is an example to all footballers.”
Weah became the first non-European player to win the Ballon d’Or while on the books of AC Milan in 1995 – helping the Italian club to two Serie A titles.
Following stints at Chelsea and Manchester City, Weah had been serving as a senator in Liberian parliament.
He was defeated by Ellen Johnson Sirleaf in the 2005 presidential race – whom he now succeeds in office.
