Appiah was handed a two-year contract this week, beating off competitions from Frenchman Willy Sagnol and Cameroon coach Hugo Broos.
Gyan, 31, worked under the 56-year-old between 2012 and 2014, during which he was named skipper of the national team.
“I am happy Kwesi Appiah has been appointed to replace Avram Grant. He is one of our own and I believe we will have to support him in this new era,” Gyan told Hot FM.
“The Ghana Football Association's six-man committee that was responsible for the naming of the coach has made their call and it’s a man who has managed the team before, so we all have to be positive and help him to succeed.
“I am yet to speak to my colleagues in the national team but I am sure they have heard and we will all be looking forward with optimism,” he said.
He added: “We will try our best to win our first game under Kwesi massively to help him have a better start. Whoever thinks Appiah is not right choice and hence won't respect him might be having short memory."
Appiah will officially begin his second stint on May 1 and his first major task will be the 2018 Fifa World Cup qualifying games against Congo. The first leg will played on August 28 at the Baba Yara Stadium in Kumasi with the return fixture slated for September 2 at the Stade Municipal de Kintele in Brazzaville.