There were no constitutional amendments that I'm aware of for the creation West Virginia, but there were congressional measures to facilitate the separation.
Ultimately, it seems that it was accomplished by a presidential decree.
The state and Congress both must act, under the US Constitution. However, when Virginia seceeded from the US, that enabled Lincoln to declare the state government to have abdicated and recognize a newly constituted alternate legislature of the state of Virginia, which then authorized the creation of West Virginia from its territory. So, the US Constitution was satisfied, without Virginia consenting in the main bit of its population.