The 53-year-old Walsh has replaced Heath Streak, who served as bowling coach for two years till May.
This is going to be Walsh's first major assignment as a coach in international cricket after he retired in 2001 as the then leading wicket-taker in Tests.
"Having watched Bangladesh cricket from afar over the years, they are a seriously talented bunch of players," Walsh said in a statement.
"Chandika Hathurusingha has done a wonderful job thus far as head coach, so hopefully, I can complement his skills and continue the positive progress," he added.
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"Obviously the West Indies is my home but the chance to go in a new direction in coaching at the international level with a talented group, was one I couldn't let that opportunity pass," said Walsh.
The most successful bowler from the Caribbean Islands with 519 Test wickets, Walsh recently completed his role as a West Indies selector.
In the past, Walsh has managed the West Indies Under-19 team and been a bowling consultant for the Jamaica Tallawahs in the Caribbean Premier League.
BCB Chief Executive Nizamuddin Chowdhury feels Walsh's mentoring will take the country's cricket to greater heights.
"We are delighted to have Courtney in our ranks. He is a role model to millions and his fast bowling knowledge is second to none. Bangladesh cricket at present is going through the best pace bowling phase in our history and Courtney's involvement I am sure will take it to greater heights," said Chowdhury.
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