The Crown Office had previously said South Lanarkshire-based Errington Cheese would not face prosecution over the child’s death.
The Crown Office said it had considered “all the relevant matters” before ruling out an FAI.
A total of 26 cases of the same strain of E. coli O157 were identified between July and September 2016 as a result of the outbreak, which left 17 people requiring hospital treatment.
A report published by Health Protection Scotland concluded in March 2017 that the source of the infection was consumption of an unpasteurised cows’ milk cheese.
Their incident management team found that potentially pathogenic E. coli were able to enter and survive the cheese production process at the food business.
However, Errington Cheese has repeatedly questioned the quality of the investigation and any suggestion that their product was responsible.