Andriy Yarmolenko's own goal ensured a 1-0 triumph for Wales, who were largely indebted to the heroics of Wayne Hennessey as Rob Page's team held on to book its spot at Qatar 2022.
It meant Wales qualified for the World Cup for the first time since 1958 and Bale, who will leave Real Madrid when his contract expires at the end of the month, was in no doubt about the significance of the result.
"It's the greatest result in history for Welsh football," Bale said. "We are all ecstatic. The fans together, it was a delight, and we are going to a World Cup!
"It means everything. It's what dreams are made of. It's what we've been working for since we first came here. I'm so happy for all our amazing fans and our country. Words can't describe how we're feeling at the moment.
"It was difficult. I haven't done too much over the last four weeks because of my back spasm, which everyone knows about.
"Contributing in whatever way I could, but the most important thing was to get through it and get through to the World Cup.
"I gave my all on the pitch and I was running a bit on empty, it's always good to have players come off the bench and do a job."
Wales' victory means they will face England, the United States and Iran in Group B in Qatar.
And interim manager Page dedicated the Red Dragons' success to former boss Gary Speed, who died in 2011.
"I've said in the build-up, Gary Speed started this 12 or 13 years ago," he told a media conference. "I want to dedicate this to Gary. He started the culture, 12 years ago.
"There was a difference, there was a change. The environment completely changed. I've inherited that, Chris Coleman took it on and took it to another level, and I've inherited that group.
"We're confident going into games now. We don't hope to qualify for the World Cup or Euros now, we believe we can do it, so there's been a massive change in the mentality as well.
"I had a difficult decision tonight. I've got people like Harry Wilson and Brennan Johnson, who is going to be a superstar, isn't he? You've got people like him who didn't start tonight. But we had our best 11 on the pitch.
"It's encouraging, it's good, we're going in the right direction. We need to continue to develop these young players that we have done for the last few years, and it's only going to get better for us."