Hinduism's Atman is the imperishable and indestructible immortal soul or self that pervades the entire body.
That which pervades the entire body, know it to be indestructible. No
one can cause the destruction of the imperishable soul. Only the
material body is perishable; the embodied soul within is
indestructible, immeasurable, and eternal. ...
Neither of them is in knowledge—the one who
thinks the soul can slay and the one who thinks the soul can be slain.
For truly, the soul neither kills nor can it be killed.
The soul is neither born, nor does it ever die; nor having once
existed, does it ever cease to be. The soul is without birth, eternal,
immortal, and ageless. It is not destroyed when the body is destroyed.
Hindu text Bhagavad Gita 2.17-20
Buddhism's Anatta is from the statement "sabbe dhamma anatta" (Dhp 279) which means that "all phenomena is not self".
So, Atman and Anatta are opposite.
Then the Venerable Ānanda approached the Blessed One … and said to
him: “Venerable sir, it is said, ‘Empty is the world, empty is the
world.’ In what way, venerable sir, is it said, ‘Empty is the world’?”
“It is, Ānanda, because it is empty of self and of what belongs to
self that it is said, ‘Empty is the world.’ And what is empty of self
and of what belongs to self? The eye, Ānanda, is empty of self and of
what belongs to self. Forms are empty of self and of what belongs to
self. Eye-consciousness is empty of self and of what belongs to self.
Eye-contact is empty of self and of what belongs to self…. Whatever
feeling arises with mind-contact as condition—whether pleasant or
painful or neither-painful-nor-pleasant—that too is empty of self and
of what belongs to self.
“It is, Ānanda, because it is empty of self and of what belongs to
self that it is said, ‘Empty is the world.’”
SN 35.85
According to the Hindu school of Advaita Vedanta, Atman is Consciousness:
Atman is all consciousness and holy, the body is all flesh and impure;
and yet, etc., - verse 19
Thus all the three states are unreal inasmuch as they are the creation
of the three Gunas; but their witness (the reality behind them) is,
beyond all Gunas, eternal, one, and is Consciousness itself. - verse 58
The wise should always think with great care of the invisible, the
visible, and everything else, as his own Self which is consciousness
itself. - verse 141
Adi Shankaracharya's Aparokshanubhuti
According to the Buddha, Consciousness is dependently originated and is impermanent. It's not the same Consciousness that roams throughout one's life and continues to another life:
The Buddha
said to him, “Is it really true, Sāti, that you have such a harmful
misconception: ‘As I understand the Buddha’s teachings, it is this
very same consciousness that roams and transmigrates, not another’?”
Sati: “Absolutely, sir. As I understand the Buddha’s teachings, it is this
very same consciousness that roams and transmigrates, not another.”
Buddha: “Sāti, what is that consciousness?”
Sati: “Sir, it is he who speaks and feels and experiences the results of
good and bad deeds in all the different realms.”
Buddha: “Silly man, who on earth have you ever known me to teach in that way?
Haven’t I said in many ways that consciousness is dependently
originated, since consciousness does not arise without a cause? But
still you misrepresent me by your wrong grasp, harm yourself, and make
much bad karma. This will be for your lasting harm and suffering.”
MN 38
The same sutta explains that consciousness arises dependent on the six sense media and their sense objects.