Ms Sturgeon announced the move as she met the celebrity chef, who has previously campaigned to make school dinners healthier, to discuss the problems of childhood obesity and healthy eating.
The two discussed action to tackle obesity and unhealthy eating, which Ms Sturgeon called "a serious public health issue which can not be ignored".
The goal is part of the Scottish government's Healthy Weight and Diet plan that will be published this summer.
Two in three adults in Scotland (65%) are overweight and obesity rates are among the highest in the world.
Nicola Sturgeon believes Scottish independence is "not off the table".
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Sturgeon also was also quizzed about the deadlock in talks between the United Kingdom and Scottish Governments over devolved powers post Brexit.
"To ensure that the steps we take are proportionate and deliver beneficial outcomes, we will consult widely with consumers, suppliers and retailers following the release of the new plan".
At present, 29% of children in Scotland are at risk of being overweight, and 14% are at risk of being obese.
It is to include action to restrict promotions and advertising of junk food, including multi-buy deals on unhealthy products.
Doctors welcomed the move with Peter Bennie, chair of the British Medical Association (BMA) Scotland, stating: "Obesity is a major public health challenge that we must do far more to address in Scotland".