The 24-year-old was finally unveiled before the Madrid public on Monday after the two clubs spent virtually the entire transfer window engrossed in a transfer battle.
Despite wanting the deal to be wrapped up quickly, Bale said that he understood the stance of Spurs chairman Daniel Levy, who he believes was doing his best by the North London club.
"It was a long time, it was very stressful to say the least," the Welsh international told BT Sport. "I knew their interest from the start and I was always confident the move would go through.
"Obviously the chairman Daniel Levy had to do his business and do Tottenham well so I kind of understood that.
"But at the same time, thinking of myself, It was a hard time, it was stressful and I just had to be patient and try and focus."
Bale will wear the number 11 shirt for Los Blancos.