The La Liga champions struck first through Cristiano Ronaldo, only to be pegged back before the interval by a brilliant goal Mario Mandzukic.
However, Madrid put on an incredible display of dominance in the second half, scoring three times to leave Cardiff with the Champions League trophy, becoming the first team to retain their crown since the modern tournament era began in 1992-93.
And Bale, who came on a second-half substitute, said he and his team-mates will savour that achievement.
“We have made history, we'll enjoy this moment now,” Bale told BT Sport.
“We needed confidence at half-time and we had to take our chances, which we did."
The Champions League final took place in Cardiff, just miles away from where the Wales international grew up and Bale had plenty of plaudits for his home country’s hosting of the event.
"What an incredible scene. The city has done an immaculate job in hosting a great event,” he said.
It has been a difficult season at times for Bale, as he only managed to play in 19 league games and lost his place in the lineup for the final to Isco. However, the 27-year-old, who had work to get fit in time for the final, is just happy to have won the title in his home country.
“To win this at home is a great feeling,” he said.
“It's been a hard season, I've worked tirelessly to get fit and these are your rewards."