adidas has seen its leadership in football eroded in recent years by the advance of its bigger US competitor Nike, which sponsors Real's arch rivals Barcelona and is reportedly in talks with Liverpool, second in the English Premier League.
The new deal is thought to be worth about €135m ($151m) per season based on a fixed fee and a percentage of shirt sales – more than twice the value of the current agreement, worth about €52m per season.
The new figure puts the club second only to LaLiga rival Barcelona as the top-earning club from kit partnership revenue.
Barcelona is understood to be making €155m per season from its kit deal with Nike, from 2018-19 to 2025-26.
Details of Real Madrid’s contract-in-progress with adidas had previously been leaked to the German newspaper Der Spiegel in collaboration with Football Leaks in May 2017.
Commenting on the partnership, Real club president Florentino Pérez said: "It is a natural step to extend our successful deal until 2028. Together we will continue to build this strategic alliance that helps us set a benchmark and remain leaders in football. Adidas is an ideal sponsor for us."