The 47-year-old Spaniard was granted an early release from his contract and is strongly tipped to take over at Egyptian giants Al Ahly.
Riveiro's final match in charge came on Tuesday night, as Pirates secured a dominant 3–0 win over Lamontville Golden Arrows at Orlando Stadium. Goals from Tshegofatso Mabasa (16'), Bandile Shandu (61'), and Kabelo Dlamini (66') gave the Soweto faithful a fitting farewell performance.
Despite his success with the Buccaneers - claiming five domestic cups out of eight and steering the team to a CAF Champions League semifinal - Riveiro made it clear his coaching journey in South Africa ends here.
"I will never coach any other team in South Africa," said Riveiro.
"I am a Buccaneer and Orlando Pirates is the only club I could have the motivation and courage, energy and heart to coach in South Africa."
Under his leadership, Orlando Pirates achieved consistent league finishes, with two second-place results and a third on the horizon.
Assistant coach Mandla Ncikazi will take over on a caretaker basis for the final four matches of the season.
"You are talking about people who have huge experience in South African football. After three years together, we have developed clear guidelines and have our methodology on how to do things," Riveiro said when asked about Ncikazi and his support staff.
"There are not going to be big changes for the upcoming four games - they [the coaches] know each other very well and they know the players, so there will be continuity.
"They know I will be there for them with whatever they need and together we will manage to finalise the season. I have zero doubt it is going to be a good month for the team."