The forward was presented as a Madrid player in front of over 20,000 fans at the Santiago Bernabeu on Monday - the day after his move from Tottenham was made official.
The transfer is understood to be worth 100million euros (£85.3million), making Bale the most expensive player of all time and surpassing the 96million euro (£80million) fee Madrid paid Manchester United for Cristiano Ronaldo in 2009.
Bale only played 45 minutes of football for Tottenham in pre-season - at Swindon on July 16 - due to injury and stayed away from the north London club's opening three Premier League games while he waited for his move to Madrid to be finalised.
Carlo Ancelotti's side have won their first three games of the new Primera Division season and next face Villarreal on September 14, a game which Bale hopes to play a part in.
There had been speculation that Real would ask Wales manager Chris Coleman to leave Bale out of the upcoming matches, in Macedonia on September 6 and against Serbia in Cardiff on September 10, so as not to risk him getting injured again.
However, speaking in his first press conference as a Real Madrid player, the 24-year-old confirmed he would join up with the Wales squad and insisted he wanted to play.
"It's not been ideal but I've been doing my fitness training and I will meet up with Wales," he said.
"I haven't had a lot of match time so that will help my fitness, as well as it being an honour to play for my country.
"It's well known I had a slight injury, which took me a bit of time, but I always wanted to be here in the white shirt of Madrid and hopefully I can get match-time with Wales and come back fit.
"I'm hoping to take it one step at a time and come back in better physical shape. I'm hoping to be involved for the game with Villarreal."
However, he pledged to work his way into the team, insisting he would not rest on his laurels after completing the move.
"I can't come in and just walk into the starting 11," he said.
"I've always wanted to improve and there's no reason that should stop now I'm here. Now I'm with the best players and the best coaches and with the best possible chance to learn off the best, I can't wait to get started."
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