The 37-year-old from Sheffield was left in a coma after the high-speed crash, which saw him being hit on the head by an airborne nose cone before he careered into a safety barrier.
IndyCar were first to make the announcement of his passing at the request of his family on Monday evening.
"This is a monumentally sad day for IndyCar and the motorsports community as a whole," IndyCar CEO Mark Miles said in a statement.
"Justin's elite ability to drive a race car was matched by his unwavering kindness, character and humility – which is what made him one of the most respected members of the paddock.
