The 40-year-old Spaniard will continue to race alongside Frenchman Esteban Ocon who was handed a fresh three-year deal by the Renault-owned team earlier this season.
The two-time Le Mans 24 Hours endurance winner and former Ferrari driver, who turns 39 this month, secured his championships in 2005 and 2006 and most recently raced for McLaren in 2018.
Alonso is hoping to become only the second driver after the late Briton Graham Hill to complete the so-called 'Triple Crown of Motorsport', having already secured wins at the Monaco Grand Prix and Le Mans 24 Hours.
The ring-like 'halo' was introduced this season to protect the drivers' exposed helmets.
We have offered Fernando a contract in the past, but that was back in 2007, said Red Bull.