The Europa League champions’ deal for Arias was reportedly dependent on Vrasljko leaving, with both moves being announced successively on Monday night.
26-year-old Arias, who started each of Colombia’s four games at the World Cup, will now battle with club stalwart Juanfran for the right-back position at the Wanda Metropolitano
He arrives in the Spanish capital after having played five seasons with PSV Eindhoven, winning three Dutch titles.
While his transfer fee has not been revealed by the club, it was previously reported that Napoli had seen an €11m bid accepted for the player before he agreed terms with Atletico Madrid.
Meanwhile, Vrsaljko heads to Serie A with his move now only dependent on “the formalization of the documents and the relevant medical examination”, according to a statement on Atleti’s website.
Inter have the option to make the deal for the World Cup finalist permanent and reports suggest they will pay a €6.5m loan fee, with €17.5m the figure to secure a future deal.
Vrsaljko, who won the Europa League last season, is understood to have asked for a return to Serie A, sparking the deals.