The versatile Matlaba impressed in a six-and-a-half year stay with the Buccaneers and was even handed the armband, but he featured less last season as Innocent Maela made the left-back position his own at Mayfair.
Ghanaian attacker Morrison spent two years with the Sea Robbers, scoring 10 goals in 43 appearances following his arrival from Congolese outfit AS Vita.
Defensive midfielder Sangweni, the younger brother of former Bucs skipper Siyabonga, is returning to Chippa after only playing three times for the Soweto giants in 2017/18.
The trio, who will link up with Dan Malesela's squad on Saturday, have been brought in to replace Ayabulela Konqobe, Sizwe Mdlinzo and Lucky Setelele at the Chilli Boys.
Defender Konqobe has reportedly been spotted training with Kaizer Chiefs.
Chippa also recently let Abel Mabaso and Linda Mntambo join Pirates, and added veteran duo Daine Klate and Thabo Nthethe to their roster among other off-season signings.