The centre-back will initially link up with the Serie A side on loan before joining for a reported €15 million fee ($24.2 million), having agreed a four-year deal.
Murillo spent the second half of last season on loan at Barcelona but started a single LaLiga game.
Colombia international Murillo was then left out of his country's squad for this year's Copa America.
Valencia has allowed him to leave only a year after he moved to Mestalla from Inter Milan.
Valencia had already signed goalkeeper Jasper Cillessen from Barcelona for 2019-2020, with Neto eventually moving the other way.