Bale, who has won two Champions League titles in three years in Spain, solidifies his position as one of the highest earners in football along with the likes of Real team-mate Cristiano Ronaldo and Barcelona duo Lionel Messi and Neymar.
The flying winger, 27, is set to take home as much as £350,000 a week after tax, according to British media, though figures vary wildly.
"That's for me to know and no one else to find out, sorry," said a smiling Balewhen quizzed on his new salary.
However, Ronaldo looks set to retain his status as top dog of the pay packets at the Bernabeu with the Portuguese expected to become the latest Madrid star to extend his deal in the coming weeks.
Real have already handed lucrative renewals to Luka Modric, Toni Kroos and Lucas Vazquez to hold onto their key men with a one-year transfer ban imposed by FIFA to come over the next two transfer windows.
Madrid and arch rivals Barcelona have embarked on a fleet of renewals to ward off interest from the cash-rich Premier League, backed by a £5 billion ($6 billion) domestic TV deal.
Bale joined Real for a then-world record fee of just over 100 million euros from Tottenham Hotspur in 2013.
That figure has since been eclipsed by Paul Pogba's 105-million-euro move to Manchester United in August.
"It's Real Madrid, it is the biggest club in the world," Bale added, rejecting any notion he could return to England, where he was crowned Premier League Player of the Year in for the 2010/2011 and 2012/2013 seasons.
"When an opportunity to play for Real Madrid comes up, you don't turn it down."
Madrid have topped the Deloitte Football Money League for the past 11 years as the highest earning club, but were overtaken last season by Barca.
Barca president Josep Maria Bartomeu confirmed at the club's annual general meeting on Saturday that contract negotiations with Luis Suarez and Messi are also under way after Neymar recently extended his deal to 2021.
