Both forms are correct. Center and centre are two correct spellings of this word, they also have the same pronunciation, which is / ˈsɛn tər /, and the same meaning. The basic difference is that center is American English spelling and centre is more common in British English. There is a large group of words with this kind of difference in endings, where the American form ends with -er and the British with -re.

Correct spelling, explanation: British English spelling.

Correct spelling, explanation: American English spelling.

Definition of center/centre:
noun: the middle part of something;
I want to put this couch in the center of the room.
– a thing, a situation, or a person that is most involving or that a lot of attention is focused on;
I hate being the centre of attention, so that is why I usually stay quiet during company meetings.
In today’s Parliament session, the center of discussion will be school reform.
– a facility that provides space for a specific kind of activities;
Have you seen the new shopping center? It is right beside the business center downtown.
verb: to put something in the middle; to fix something at or around an area;
The title and the picture have to be centered on the page.
– to give basis to something;
I centered my focus on getting the financial scholarship, this is all I can think about lately.