Bale secured a world-record switch from Tottenham on Sunday and was unveiled at the Bernabeu on Monday after signing a six-year deal with the club.
Former Wales assistant Saunders, who coached Bale while John Toshack was national team manager, believes the 24-year-old will add huge quality to Real's squad.
"Forget the money they have paid for him, they have almost sealed world dominance," he told BBC Sport.
"Imagine, you have him coming down one side and Ronaldo coming down the other side, good luck!"
Thousands of Real fans turned out for Bale's unveiling and Saunders feels the decision of Bale to briefly speak Spanish during the parade will endear him to the club's fans.
"Gareth has done the press conference in Spanish, which immediately makes everyone in Spain respect him and like him," he added.
"He has done the right thing there and he has had some good advice."
Bale featured just once for Tottenham during pre-season and has not played a competitive match since the end of last term, with Andre Villas-Boas lamenting a lack of fitness for the forward.
However, he could make his first Real appearance against Villarreal on September 14.
