The phrase 'it varies depending on' is correct and usable in written English. You can use it when describing differences in something based on a set of circumstances. For example, "How long the project takes to complete varies depending on how complex the task is.".
I don't have room to describe their work here, and it varies depending on political orientation.
"It varies depending on where you are and what site you're trying to get to," he said.
Harris has his own routine while the Mets are in the field, though it varies depending on the ballpark.
Dr. Wilbur Gould, of Lenox Hill Hospital, said that his responsibility is to the patient, but it varies, depending on what is required of the performer.
However, this relationship differed when examining one individual landscape type, it varied depending on the different landscape types.
(It varied depending on the query, in tests). .
Many reported not knowing their monthly income or that it varied depending on how many animals or animal products they sold.
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MA of Applied Linguistic, Maquarie University, Australia