The former Golden Arrows man, who has been hampered by injuries in recent seasons, has fallen out of favour at the Tshwane giants.
The emergence of Asavela Mbekile and Thapelo Morena at right back at Sundowns followed by arrival of Anele Ngcongca has not made things easier for Zwane.
His last appearance for the club came in the 3-1 defeat to Orlando Pirates, a game he didn’t finish after he was substituted midway through the second half.
Zwane joined Sundowns along with then Arrows teammate Bonginkosi Ntuli at the start of the 2013/14 season.
He helped the club to their first league title after seven years and followed it up with a Nedbank Cup crown the following campaign.
The right-back will also go down as one of the influential individuals that secured the club’s first-ever continental title in the Caf Champions League in 2016, which they followed with the Super Cup the following year.
The 32-year-old’s time at Chloorkop has seen him make 50 appearances in all competitions in the star-studded side.
Apart from his right-back position, he has been used as a left-back and centre-back at times by Pitso Mosimane.
He joins an Ajax side, who has a grown reputation for mixing youth and experience, it’s no doubt that Zwane will come handy in that regard.
With Muhsin Ertugral at the helm, who worked with him at Arrows, he will look to build his team around individuals such as the Pietermaritzburg-born defender.
Zwane was linked with Orlando Pirates at the beginning of the current season, but the move never materilized.