There is one gene pair that determines the base color of the egg, which is either blue or white. The blue shell gene is dominant, so if just one of those genes at that gene pair is blue, the egg will be base blue. If both genes at that gene pair are not-blue, the egg shell will default to base white. The not-blue gene does not paint the eggshells white, it allows the natural colors of the materials that make up the egg shell to show. The blue shell gene does color the shell blue all the way through the thickness.
Using uppercase "O" to symbolize the dominant blue eggshell gene and lowercase "o" to symbolize the default not-blue gene, your leghorn will have "oo" at that gene pair and will give one of those to all his offspring. The Ameraucana will have "OO" at that gene pair and give an "O" to all of her offspring, so the offspring of that match will have "Oo" and all pullets will lay a base blue egg.
There are many different gene pairs that affect brown on an egg. Some are dominant, some recessive, some partially dominant, and some only have an effect if certain other genes are present. The way they go together determines what shade of brown goes on the egg. The number of possible combinations is why you can get so many different possible shades of brown.
Brown and green eggs are simply brown applied on top of base white or blue eggs. One way to show that is
Base white + no brown = white eggs
Base white + brown = brown eggs
Base blue + no brown = blue eggs
Base blue + brown = green eggs
If the chicken has none of these brown genes then they cannot pass any down to their offspring.
Your leghorn should have the genetics for white eggs which means no brown genes to pass down. Your Ameraucana should have the genetics for blue eggs which means no brown genes to pass down. Those are breed requirements. As long as your two have the genetics their breeds are supposed to have there will be no green eggs. They will be blue.