Ronaldo attended Juve training for the first time on Monday after the five-time Ballon d'Or winner left European champions Real Madrid in a €112 million (£100m/$131m) deal earlier this month.
Chiellini – in the United States for Juve's clash against the MLS All-Stars on Wednesday – doubted the Italian giants would sign Ronaldo when rumours first emerged.
"[The first time I heard about Ronaldo], I said to my friends, 'Nah, it's impossible,'" Chiellini told ESPN. "After one day, [I thought] maybe it is possible.
"With our manager, with our director ... it's a reality. Juventus is growing ... year after year, and we need a champion like Cristiano.
"We are excited, we are ready to work with him; all the parts of the club, the players, the marketing manager, the director, are ready to improve with Cristiano and we hope he can help us to achieve our target."
It has been a busy off-season for Juve, who are seeking to win the Champions League, having dominated domestically with seven successive Serie A titles.
Joao Cancelo, Mattia Perin and Emre Can have arrived, while striker Gonzalo Higuain and defender Mattia Caldara could leave as Juve try to re-sign AC Milan centre-back Leonardo Bonucci just one season after the Italian left Turin.
"Leonardo, for me, is a friend," Chiellini said. "I pass my holiday with him and my family.
"I know about his quality, but I don't know. It's not easy, and I want to have respect to my team-mates ... I'm not president or director, so we will see what happens at the end of the Serie A — we will see if Leonardo is here."