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According to this, the translation would be:

あなたは わたしの こころに います。

That seems simple enough. However, the same source claims it's not in use, and recommends the following instead:

いつも　あなたのことを　おもっています。

I don't get how it's the same.

The first one implies romantic feelings, while the second one can mean anything.
There are many reasons for thinking about someone.

Culturally, Japanese people are not as publicly direct about their deepest feelings. In English speaking cultures, we use the phrase "I love you" a LOT. It can be for an intimate relationship, or it can be used for a best friend with no romantic undertones. You won't hear the Japanese people say 愛している the same way Americans tend to use the English equivalent.

This is because in Japanese culture, you tend to 'beat around the bush.' In other words, the Japanese language isn't as direct in what they say... At least in literal translation. Once you get the hang of the culture, you'll get used to the indirect directness of the Japanese language.

Let's break down the second sentence a little bit to help you understand what's going on here.

いつも- Always, or at all times.

あなたのこと- literally translated as your things. In general usage, however, we can take this to mean everything about you. I would take this to include physical and emotional characteristics of the individual in question.

を- object marker.

おもっています- to be thinking about. Used in combination with いつも, you get the implication that you hold what you are thinking about dear to you... in your heart if you will.

Bringing it all together, you get the literal translation:

I'm always thinking about you.

But if we add on to the sentence to capture true implications of what is being said (indirect though it may be):

I'm always thinking about you, your smile, the way you laugh, your beauty, everything. (I hold these thoughts dear to me.)

All things considered, I think that this is an appropriate Japanese approximation of You're always in my heart. You'll find this frequently in studying different languages, but sometimes English idioms are translated completely different in Japanese. See this question, for example.

Finally, this is a prime example of my final point. You will find that often in Japanese, what is implied carries a lot more meaning than what is said. So just because something doesn't appear as direct as you expect doesn't mean that it isn't. It is easy for the Japanese learner to be deceived in this respect.