Bale, without a club following his departure as a free agent from Real Madrid last week, saw his first-half free kick against Ukraine deflect off the head of Andriy Yarmolenko to seal a 1-0 playoff victory in Cardiff to end Wales's 64-year wait to qualify for the World Cup.
"Maybe for a little bit!" Bale said. "The result is the greatest in Welsh football history. We're going to a World Cup!
"It means everything, what dreams are made of, we've been working towards it since I first came in here. Words can't describe how we feel at the moment.
"It's what we've been working all our careers for and to do this for the fans, the nation, ourselves and our families is an incredible achievement, and it will be something that we will be forever proud of.
"It means everything. It is the last piece of the jigsaw that we all wanted and we're going to celebrate well tonight."
Nine saves by goalkeeper Wayne Hennessey were crucial as Wales held off fierce Ukraine pressure to win and he said it was the best game he had played for his country.
"Everyone on the pitch tonight was amazing," Hennessey said. "That's the best game I've had in a Welsh shirt, I'm buzzing.
"We're a small nation, and it's great to take everyone to a World Cup."