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Photo of Demi and Alex courtesy of Facebook

Demi Lovato has agreed to pay off Alex Welch ... the dancer the Disney starlet punched in the face back in October, according to TMZ.

The young female dancer will receive a financial settlement, however the amount has not been disclosed.

Donald Karpel, Welch's lawyer, tells X17online, "Any and all issues and disputes have been completely and amicably resolved with Demi Lovato."

As for how Welch is feeling in relation to the injuries inflicted by Lovato, Karpel adds, "She's doing better. She's fine."

The attack took place on a private jet while Lovato and her dancers were on tour with The Jonas Brothers. Soon after the incident, photos surfaced of Welch's injuries ... including a bruised eye.

Demi is currently in treatment at Timberline Knolls in Chicago, Illinois. As for the settlement, Lovato's rep tells X17online, "Not going to comment."