* Mayor to step down early in December after 13 years
* Wowereit long one of Germany's most popular politicians
* His reputation hit by debacle over delayed Berlin airport (Adds Wowereit comments)
By Alexandra Hudson
BERLIN, Aug 26 (Reuters) - Berlin's mayor Klaus Wowereit is stepping down after 13 years running the city he once described as "poor but sexy", his reputation tarnished in recent years by embarrassing delays and cost overruns to the German capital's new airport.
Wowereit, who became a national celebrity by coming out as gay during his first mayoral election campaign just as a newspaper was planning to expose his sexuality, is leaving two years before the end of his term.
Facing the media on Tuesday with a typically broad grin, the 60-year-old mayor said: "I announced to the Senate today that I will not stand again for the next legislature period and that I will vacate my position on Dec. 11."
After much speculation about how long he would continue Wowereit said he had wanted to give some clarity.
"This was not an easy decision. I have been in politics in this city for more than 40 years... it is sometimes difficult to find the right time to go. For me the time has come now. I'm going of my own free will and I'm proud of having played my part in the positive development of this city."
Dubbed "Wowi" in the media, the Berlin-born politician's candour, smile and down-to-earth manner made him one of Germany's most popular politicians, and he was frequently photographed hobnobbing with celebrities and enjoying a party lifestyle.
Seen by some as a possible SPD candidate for chancellor, he was ultimately passed over due to party concerns that what made him popular in Berlin might not play so well with voters nationwide and because of a perceived lack of gravitas.
Tagesspiegel newspaper said Jan Stoess, head of the SPD in Berlin, would take over from Wowereit, who had won a third term as mayor in September 2011, governing in coalition with Chancellor Angela Merkel's Christian Democrats (CDU).
POOR BUT SEXY
Wowereit's phrase "poor but sexy" was a marketing stroke of genius for the city, which has transformed into one of Europe's hippest and most popular tourist destinations on his watch.
"Berlin is the place to be for people from all around the world," Wowereit said. "Together we can be proud of this in the last years we have taken a huge leap forward."
Berlin is finally starting to glimpse the prosperity that was supposed to land in its lap after the Berlin Wall came down in 1989 and it was restored as the jubilant capital of Germany after decades of Cold War division.
Noting the looming 25th anniversary of the fall of the Wall on Nov. 9, Wowereit said: "Berliners have achieved a huge amount in the last 25 years to turn the once divided city into an international metropolis. This wasn't always easy... but ultimately it has been very successful."
The city remains a work in progress. The centre is a mess of torn-up streets and construction. Berlin does not dominate decentralised, federal Germany the way London or Paris do their own countries and it generates just 4 percent of German output.
However its economy is growing faster than the German average and it has one of Europe's liveliest digital start-up scenes. Shopping centres and luxury housing are going up on the former 'no-mans land' by the Wall and the population is growing fast, though at 3.4 million it is still less than in the city's early 20th century heyday.
The city's building boom and rising popularity make it all the more embarrassing that it still does not have an airport befitting a capital city. The new international airport - a pet project of Wowereit's - is running five years behind schedule, at twice the original budget, and has become a national joke.
"One of the biggest defeats of course, was the non-opening of the airport. That was a bitter defeat and remains so, and I hugely regret that this still hasn't been put right," the mayor said.
Wowereit suffered another defeat in May when Berliners voted in a referendum to reject the Senate's plans to partially build on the historic Tempelhof airfield. "Would you trust this man with another airport?" read the campaign slogan to save the airfield, beneath a picture of Wowereit slumped back in a chair.
But SPD leader and vice chancellor Sigmar Gabriel said "that Berlin today is an open, tolerant and attractive world city, on the right path economically, is down to Klaus Wowereit".
Berlin's debt to capita ratio is twice the national average however, and nearly 17 percent of Berliners rely on welfare. It is also struggling with high unemployment and resentment at the rapid gentrification and an influx of tourists. (Editing by Stephen Brown and Noah Barkin)