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The Canada international, was born to Liberian parents in a refugee camp in Ghana after they fled their home country due to civil war.
Davies and his family were resettled to Canada when he was five, and at 16 he became the youngest ever player to represent the country's national team.
He is the first footballer to take on such a role with the UNHCR and vowed to help give refugees around the world a voice.
Davies told the agency's website: "I am proud to join the UN Refugee Agency as a goodwill ambassador. My own experiences make me want to speak up for refugees, to share their stories and to help make a difference.
"Whilst the refugee camp provided a safe place for my family when they fled war, I often wonder where I would have been if I had stayed there and not benefited from the opportunities I got thanks to resettlement.
"I don't think I would have made it to where I am today. I want people to know about the importance of helping refugees, wherever they are, in camps or cities, in neighbouring countries or countries of resettlement such as Canada.
"Refugees need our support to survive, but also access to education and sports, so they can fulfil their potential and truly thrive."
UNHCR head Filippo Grandi added: "Alphonso personifies the power of sport and we are truly honoured to have him joining us.
"Sport has the incredible power to bring hope, to heal and to help shape the future for those forced to flee. In our work with refugees, we see daily what uplifting difference sports can make in their lives.
"His personal story, his talent and triumph as a professional footballer and his commitment to help refugees is impressive. I am looking forward to working with him."
Davies joined Bayern from Vancouver Whitecaps in July 2018 and was a key part of their 2019-20 treble-winning campaign and subsequent Club World Cup victory.
He has played 52 matches in the Bundesliga, tasting victory on 39 occasions, with five goals and six assists in the competition.
Davies has one goal and one assist, from 15 chances created, in the 2020-21 season.