The Spanish international also highlighted the dedication of United fans who traveled to Madrid.
"The passion of everyone who traveled to Madrid was incredible; that atmosphere stayed with me and I can't wait to represent them every time I step onto the pitch," she said.
Medina expressed her readiness for the next stage of her career.
"I am ready for the next stage of my career and to show my qualities in the intensity of English football," she added.
Medina will wear the number 6 shirt for United.
She developed through the youth ranks at Sevilla and Camas before making her top-flight debut for Real Betis at age 15.
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She later moved to Atletico Madrid, where she made over 100 appearances and won the Copa de la Reina.
