The South African Club announced on Monday that a deal had been agreed with the Parkhead outfit for the sale of the Bafana Bafana star.
The defender who has played his entire career in Cape Town first made his debut for the South African national team when he was just 17 and has gone on to have 19 caps under his belt.
“When Michael Makaab Jr told me that Celtic was interested and I knew that Brendan Rodgers was the coach, I couldn’t believe it,” Coetzee told Soccer Laduma.
“It’s every footballer’s dream to play in the Champions League, and I have the opportunity to do that now. It’s up to me to make full use of it.
“I’m over the moon. It’s something that I’ve always worked towards since I joined Ajax, and now it’s happened. I think that it’s the right time and the right club.
“I met with the Celtic scout, and he showed me some videos about the club, supporters and facilities. I think it’s the best option because the coach believes in youngsters and the type of football they play, coming out of the back, suits me nicely.
“I don’t think that I need to work on anything physically, I think my body is right the way it is. It’s not about being physical, sometimes you need to be a bit more aggressive but I’m not really that kind of player. I’m just going to go there and play my football, that’s why they’ve signed me. The coach will advise me on what I need to work on.”