Breaking temporary job contract to work full time

I apologize for being so out of sorts, but I am in a pickle and I genuinely don't know what to do! I am working as a contractor with a company through Kelly services, but I was recently offered a job working in a different department at the company that I am loaned out to now. I want the full time position, but I am afraid of what could happen if I leave my contract early. I do not know what could happen. I want to contact HR for the loanee company but i feel I should contact my recruiter and let them know what I want to do.

Any advice or help would be great!

I live and work in the USA.

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