The national team's greatest result is the World Cup play-off victory over Ukraine, says Bale.
The talismanic forward made the difference when his 34th-minute free- kick was headed into his own net by Ukraine captain.
Wales hadn't been to a World Cup finals in 64 years.
Bale said it was the greatest result in Welsh football history.
It means a lot. Dreams are made of that. I'm so happy, that's why I'm speechless.
Words are not enough to describe how we feel.
Wales will play England, USA and Iran in a group at the World Cup in November.
Bale said it was hard to put it into words on the radio.
It will be something that we will be proud of for the rest of our lives, because it's what we've been working for and to do this for the fans, the nation, ourselves and our families is incredible.
It means a lot. We're going to celebrate tonight because it's the last piece of the puzzle.
Wales manager Rob Page said on Sky Sports: "I'm so proud of the guys, they thoroughly deserved it."
The boys were missing the World Cup, and now they have it.
They helped us from the beginning.
I had full confidence in the guys when I saw what they did in training.
The other side of the coin was the end of the Ukrainian fairytale, which was to reach the World Cup finals for the first time.
A nation torn apart by war since Russia's invasion a little more than 100 days ago received much needed cheer when they beat Scotland in the semi-finals.
Oleksandr said that every one of them gave everything.
The goalkeeper for Wales is definitely the man of the match, he did a great job.
I don't believe we deserved to lose, but that's football.
Emotions are what football is about. Unfortunately, we didn't get the result we wanted, but we can still bring some emotion to our fans.
Footballers need to represent our country as best they can.
We need to stop the war, everyone needs to live in peace. Who knows if we'll stay together tomorrow.
I wish Wales the best of luck in the World Cup.