The seamer, despite suffering a stress fracture of his back in August, had previously travelled with the squad but was not officially part of it during the first Test at the Gabba.
The 28-year-old stayed behind in Brisbane, but marked his comeback for the Performance Programme against Queensland 2nd XI last week with an unbeaten half-century and four first-innings wickets.
While his return to the full squad was expected as a result of his display, the England and Wales Cricket Board confirmed his official inclusion on Monday.
A statement via the ECB's text service read: "Tim Bresnan has been added to the England Test squad following his recovery from a back injury, and is available for selection."
The second Test gets underway at the Adelaide Oval on Thursday with Australia holding a 1-0 lead.