Wales convincingly beat defending champions Ireland 25-7 in Cardiff at the weekend to claim the Grand Slam and a first Six Nations triumph since 2013, and Warburton says the side now have no peer, bar, perhaps, New Zealand.
"Wales deserved to win this and it sets them up so nicely. I don't want to get too excited but, because South Africa and Australia are not the sides they once were, Wales have a real chance in the World Cup," Warburton wrote in his column for The Times.
"If somebody else beat New Zealand and knocked them out of the tournament, as a Welsh fan you would be thinking, "Oh my God, this is on." Basically, New Zealand are the only team I would really worry about Wales playing."
But Warburton also stressed that international rugby is a tough environment and fortunes can swing quickly, though Gatland will be well aware of the pitfalls.
"When we last won the Grand Slam in 2012 we then went to Australia and lost all three Tests, even if they were all desperately close. Suddenly we went on an eight-game losing streak. Things can change quickly. Gats will know that."
Warburton, who retired last year at the age of 29 due to injury, but with the most number of caps as Wales captain, says Gatland has been building his team on and off the pitch for a number of years.
"He now has more resources in Wales and the depth he has created is no accident. He puts more faith in youngsters and untried players than other coaches. He has tried some who have not quite made it but his success rate is high.
"Take even Liam Williams. People forget that 18 months before Gats picked him he was a scaffolder. Now look at him.
"Gats converted Jamie Roberts from a full-back/wing to a centre. He gave George North his chance at 18, Leigh Halfpenny his chance at 19. He took a punt on me as a young captain at 22.
"It is hard to do all that when you are under the pressure of the Six Nations and the autumn series when you have got to deliver."
Warburton believes Gatland's best work off the pitch has been to raise expectations and those will be at fever-pitch come the World Cup.
"He has simply changed the psychology of the nation. He took over a nation of underachievers and now we expect to win the Six Nations every year. His first impact was on the players, obviously, but that has found its way all the way down to the fans.
"Wales are now a team of achievers and the nation wants and believes that the team can achieve."