The German-born 24-year-old is set to sign a contract that will see him remain at Signal Iduna Park until 2019.
Dortmund sporting director Michael Zorc revealed Kampl was a player who had been on the club's radar for a long time.
"Kevin Kampl is a versatile attacking-midfielder, who we have been observing for some time," he said. "His style of play fits in perfectly with our own."
Kampl has scored 29 in 109 appearances for Salzburg in all competitions, and has won 14 caps for Slovenia.
News of Kampl's arrival follows the announcement that striker Ji Dong-won is set to depart Dortmund for Augsburg.
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