Training sessions for the swimming leg of the triathlon were cancelled due to poor water quality in the Seine and the men's event was put back to Wednesday last week, taking place on the same day as the women's.
Organisers confirmed that the relay would take place on Monday, despite cancelling training yesterday.
"A meeting was held... to review the water quality results," World Triathlon and the Paris Games Organising Committee said in a joint statement.
"During this meeting, World Triathlon took the decision to confirm the mixed relay competition..."
Belgium, however, will not take part after one of their athletes, Claire Michel, fell ill.
"Claire Michel, a member of the relay team, is unfortunately ill and must withdraw from the competition," the Belgian Olympic Committee (COIB) said in a statement.
"The COIB and Belgian Triathlon hope that lessons will be learned for future triathlon competitions at the Olympic Games."
The COIB released another statement to clarify that Michel was back in her room at the Olympic Village.
"We have seen various statements in national and international media with incorrect information," the second statement said.
"Please note that Claire Michel has not been in the hospital for four days. Furthermore, she was not hospitalised prior to today.
"It is correct that she was taken to the polyclinic in the Olympic Village earlier today for treatment."
World Triathlon said it had not heard from the Belgium team about withdrawing from the event.
"The team... chose their position on the pontoon this morning and checked-in their bikes ... We have not received any other communication from them," a spokesperson said.
Paris 2024 organisers wished Michel a quick recovery and said the water quality of the Seine on the morning of the women's race, in which she finished 38th, was very good.
"Paris 2024 wishes to remind everyone that the health and wellbeing of athletes is our top priority," the organising committee added in a statement.
"Water samples... on the morning of the individual triathlon events showed the quality to be at a level considered "very good" by World Triathlon's criteria, according to results analysed and released the following day."
