What do atheists feel about meditation and its positive health effects? Is there something like "atheist meditation"?

Yes.  Atheists do everything humans do except believe in gods.

Mindfulness meditation or, as many call it, living in the moment.

Atheism is a specific belief on a specific issue: the existence of <insert god here>.  It does not directly correlate to meditation or any of various types of institution. There are some atheists who enjoy meditation, and there are some atheists who do not.  I personally enjoy when I have the free time, rare as it is with an infant, to sit down and be still.

Meditation has no religion

I'm an atheist and can speak only for myself. I meditate. I believe it helps my physical, emotional, and yes ... spiritual health. It helps me to maintain a reasonable perspective on life and its challenges.

Most http://liveanddare.com/types-of-meditation can be practiced without having any belief as a requirement for it. It's basically learning to control and focus your own attention. There are many atheists that practice it, either for the purpose of http://liveanddare.com/benefits-of-meditation/, or for personal growth.

Whatever union between theism and meditation you see, it is purely a product of imagination. I would consider myself an atheist--really I believe more that if there is a "God" or "gods" it doesn't matter: my morality is unchanged as I wish to be decent to all people and beings no matter the existence or non-existence of anything else. Too, the concept of eternity is something that I have not witnessed anywhere and so it seems to me a wholly invented, never realized concept. So I am atheist by Occam's Razor, if you wish. Though, again, it doesn't really matter. Meditation is the most important of my daily habits. The benefits I receive from my practice are many and include gaining increased patience and acceptance for those who choose to live their lives in ignorance. For the past month, I have been meditating on the rose plant--watching it grow, understanding it's life cycle, etc--to gain insight from the plant. Through this, I have gained a greater connection to myself, deeper acceptance and love for myself and as a result greater acceptance and love for all beings. With the accompanying diet for this meditation, my self-discipline has grown massively. I've studied various forms of meditation through the years though I am expert in none of them. But I can say I have seen few forms of meditation that require any belief in "God" or "gods". I have seen, however, forms of meditation that specifically ask the meditator not to abandon their belief in God or gods, but to not bring those beliefs to the cushion. And so I again say that whatever union you perceive to exist between theism and meditation is an illusion. Not to worry: most things are such illusions.

Real meditation is devoid of any religious sound, symbol or image. Even if one starts with a religious meditation and uses a symbol etc, finally the meditation means being free from all. The goal of meditation is nirvana (as achieved by Buddha) , kaivalya ( as per Yoga) or enlightenment which is same whichever religion you may follow or not follow any religion. In fact following an organised religion can be a hindrance in achieving enlightenment more often than not.

That is a really vague question! What does meditation have to do with religion? Yoga, meditation, astrology, ayurvedic medicine etc are often associated with religion, as they are traditional concepts. As an atheist, I do believe all the concepts I mentioned above have some degree of truth to it, and can be beneficial if done correctly, with or without a religious bent.