"Такой и есть" is correct. But it used rarely. For example you open the parcel with a chinese mobile phone inside. You open it and see that its screen is 4,5" wide and you say to your friend who stands near you: "I am sure, it should be 5" wide", but your friend says: "No, you are not right, он такой и есть".

To understand it better, you could put the word "такой" at the end. "И есть такой/Такой и есть." mean "Он такой"-It/He is like this/that. "Такой и есть" is used to make the statement "It/He is like this/that" sound stronger. For example, someone doubts that something or someone is like this/that. You say, You can be sure, it/he is just like this/that.-Не сомневайся, такой и есть.

"Такой и есть" is wrong, "Такой, какой ... есть" is right. It means like "as is" I'll write preferred variants of using the phrase: "Я/Ты такой, какой я/ты есть". "Я/Ты такой, какой и есть*. Он такой, какой и есть. "Она такая, какая есть". "Она такая, какая и есть", ("Она такая, какая она есть" sounds awful (second "она" has 2 stresses and it's uncomfortably to say the word with "какая")). I never heard "Оно такое, какое есть". I can't even come up with any example using the word "оно". "Мы/Вы/Они такие, какие и есть".