Big Ben is the London landmark traditionally used for the New Year's Eve midnight countdown chimes.
Big Ben is the nickname commonly used for the Great Bell of the clock at the Palace of Westminster. Strictly speaking, the name refers to the bell, not the entire clock tower, which was renamed the Elizabeth Tower in 2012. The bell's deep strikes are associated with major national moments and are broadcast during the transition into the new year when conditions and broadcasting arrangements permit.
London's modern celebration also includes a large fireworks display along the River Thames, with views around the London Eye, the South Bank, and Westminster. The fireworks and the bell are related parts of the city's New Year's coverage, but they are not the same landmark. The London Eye is a viewing structure and a visual centerpiece, not the source of the traditional chimes.
The Great Bell was cast in 1858, and the clock began operating in 1859. Because the tower may undergo maintenance or the broadcast may use recorded or relayed sound, the exact presentation can vary, but Big Ben remains the canonical answer to the countdown question.