Chilean newspaper La Stampa states that the Gunners have agreed a £21m deal for the player, who is currently playing at the Copa America.
Reports last week suggested that Gunners playmaker Alexis Sanchez, a close friend and international team-mate of Vidal's, had "convinced" him to join Arsenal.
Sanchez had offered support to Chile's captain Vidal after he was recently charged with drink-driving after smashing his Ferrari while at the tournament, which is being hosted in Chile.
"We are a family and we are there to support him," the 28-year-old Gunners forward had said. "All the players were with him.
"The important thing is that Arturo, his wife and everyone else are well. The case of Arturo should now close and we can concentrate on the Copa America."
Sanchez had also defended his team-mate after the incident by posting pictures of them together on both Twitter and Instagram.
Chile face Peru on Monday in the semi-final of the competition.
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