Booysen joined Ajax on transfer deadline day as part of a player-plus-cash deal that saw fellow centre-back Coetzee move to African champions Mamelodi Sundowns.
The 29-year-old came through the Urban Warriors' development ranks a decade ago, and went on to have spells with SuperSport United, Maritzburg United and Sundowns.
Booysen also recently captained a makeshift Bafana Bafana outfit in 2018 African Nations Championship (CHAN) qualifiers against Botswana and Zambia.
Booysen told Ajax's website: "Rivaldo did really well for Ajax Cape Town, applied himself well and I wish him all the best at Mamelodi Sundowns.
"Yes, I do bring experience, we have different qualities, but for me at the end of the day it is about the team and to help the team. I come here as a leader, but I also want to learn from my fellow teammates and I feel that the quicker we adapt to one another the better for the team. It is all about getting the results at the end of the day.
"For me it is about giving advice in the right way and helping the youngsters around me. The senior guys have to stand together and lift the team. Not a good start to the [2017-18 Absa Premiership season], but all is not lost and there is still a very long way to go.
"The togetherness and brotherhood will continue to grow. On a personal level, having captained Bafana Bafana – coming here, it can only help me grow as a player. We must grow as a team and I am looking forward to the challenge and helping the team."
He does not anticipate any problem adjusting to the coaching methods of Dutchman Stanley Menzo.
"We had a chat and obviously I understand the Ajax Cape Town way of playing. He took some time to explain to me his philosophy and his way of playing. For me it is all about understanding what the coach wants.
"Yes, I have been around the block, but I am open to learning. I want to learn and I am open to take advice from the coach as at the end of the day we have to apply his tactics.
"It has been good, I came through this system – it is like riding a bike again. I worked with coaches similar to coach Stanley like Foppe De Haan, it is not a different environment. At the end of the day football is football – it is the same language. I am eager to continue growing as a footballer under coach Stanley."