The Bull of heaven was sent to earth by the goddess Ishtar, to destroy Gilgamesh. But Gilgamesh thwarts the bull and kills it.
There are two versions of the incidents that happened next.
From Sky Script:
Gilgamesh triumphed over the Bull, which was then placed in the heavens, but for his sacrilege the gods declared that the life of his best friend, Enkidu, should be taken as a forfeit.
This particular extract indicates that, after its death, the bull rose to the heavens, receiving a place in there.
The other version, from Sydney Observatory:
However, Gilgamesh is able to use his heroic strength to slay the giant creature, and offers its heart to the Mesopotamian sun god, Shamash.
This extract, tells that it was Gilgamesh who presented the bull to the Sun god. But it is not clearly mentioned whether it was Shamash or some other being, who placed the bull of heaven as the constellation.
Hence from both cases, it is certain that it was indeed the bull of heaven which became the constellation known as Taurus.