Dominguez took power in 2016 after his countryman Juan Angel Napout was arrested in Switzerland as part of the FIFA corruption scandal.
Napout's two predecessors were also detained and accused of taking bribes in return for guaranteed TV and publicity contracts.
Dominguez has sought to restore the image of an institution discredited by the arrests and notorious for its lack of accountability and openness.
"I promise that all monies generated by this administration are going to be transparent and are going to be transferred to football where they should have always gone," Dominguez, who was elected for a four-year term, told delegates.
The 46-year old wants to make CONMEBOL, which has 10 members, including World Cup winners Brazil, Argentina and Uruguay, more like its European counterpart UEFA.
The confederation decided earlier this year to hold the final of the Copa Libertadores, South American equivalent of the Champions League, at a neutral venue and abandon the home and away format in use since the tournament began in 1960.
It has also petitioned FIFA to increase the number of teams at the 2022 World Cup from 32 to 48 and is backing a joint bid by Argentina, Paraguay and Uruguay to host the 2030 tournament.
(Writing by Andrew Downie; Editing by Ian Chadband)
