The 20-year-old Kenyan snubbed Alex McLeish to sign a four-year contract for the Parkhead club in a deal reportedly worth £900,000 to Belgian club Germinal Beerschot.
Wanyama, who made his Hoops debut when he came on against Cardiff City in the midweek friendly in Wales, said: "Aston Villa were interested but I chose to come here.
"I chose Celtic because I really wanted to win trophies and Celtic are a great club, an historical club.
"European football was another reason. Aston Villa aren't playing in the Europa League and Celtic will be.
"It was an easy choice for me."
Wanyama, who is in Neil Lennon's squad for Sunday's Scottish Premier League opener against Hibernian at Easter Road, chose number 67 to show his appreciation to the Celtic team which beat Inter Milan in the final of the European Cup in 1967.
He revealed that he sought career advice from his brother, McDonald Mariga Wanyama - who plays for Inter.
Wanyama said: "I spoke to my brother and he helped me to choose Celtic.
"He told me this was a great step for me and I would have the chance to win trophies.
"But he didn't know about 1967.
"I have been reading about Celtic's history and it was me who told him about it."