Born in Vigo, Galicia,[2] Riveiro began his coaching career at an early age, and took over his first senior team, CD Teis in the regional leagues shortly after. After three years in charge of the team, he spent two seasons as an assistant and coach of Rápido de Bouzas' youth categories before returning to Teis.
In 2010, Riveiro was appointed manager of Mondariz FC in the Primeira Autonómica (sixth division), achieving promotion to the Preferente in his first campaign. While in charge of the club, he was also a coach of CD Choco and RC Celta de Vigo's youth categories.[3]
Finland
Riveiro resigned from Mondariz in May 2014,[4] and moved abroad in July to work at Finnish side FC Honka, as an assistant coach.[5] In April of the following year, he moved to fellow league team PK-35 Vantaa, also as an assistant.[6]
On 7 June 2016, Riveiro was appointed assistant manager of HJK Helsinki.[7]
On 5 October 2018, he was named manager of FC Inter Turku.[8] In his first season in charge, Riveiro led Inter to the 2nd position in the Veikkausliiga, qualifying the side to a European competition after six years. On 25 September 2020, he renewed his contract for the 2021 campaign.[9] For the 2022 season, Inter replaced him with Miguel Grau.[10]