* 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 background, detail)
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.
Sources in his party, the Social Democrats (SPD), said 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, would announce later on Tuesday that he plans to step down in December, nearly two years before the end of his term. No reasons were given.
The 60-year-old's candour, broad smile and down-to-earth manner made him one of Germany's most popular politicians, and he was frequently photographed hobnobbing with celebrities.
He was seen by some as a a possible SPD candidate for chancellor, but was 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 political gravitas.
German paper Tagesspiegel said Jan Stoess, head of the SPD in Berlin, intended to 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).
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 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.
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 in their own countries and it generates just 4 percent of national 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. (Editing by Stephen Brown and Noah Barkin)