"Way to go!" is an idiomatic expression. It is not grammatically correct. It might be shortened form of "That's the way to go!" It means "Well done!" It is an expression of congratulation or admiration. It is common to follow it with the name of the person being praised. For example, if someone named Matt scores a goal in a football game, you might yell, "Hey! Way to go, Matt!" It's hard to tell from context, but a person might want to congratulate THEMSELF and phrase it as "Way to go, me!" This would be a kind of joke. "I threw a piece of trash all the way across the room! It landed in the wastebasket on my first try! Way to go, me!"

“Way to go”means someone did very well ,it is an expression used in oral English.For example,"you finished this difficult task,way to go!".But "way to go me" is not a correct expression in both oral and written English.Maybe it is a name of a song or other things.

The others are correct. Adding ME to the end: "Way to go me" is a funny way of congratulating yourself. "Wow, I actually passed that test. Way to go, Me."

It's the expression that is used to praise someone as in "Well done"