Pittsburgh is the second-largest city in the U.S. Commonwealth of Pennsylvania and the county seat of Allegheny County. Regionally, it anchors the largest urban area of Appalachia and the Ohio River Valley, and nationally, it is the 22nd-largest urban area in the United States. While the city is historically known for its steel industry, today its economy is largely based on healthcare, education, technology, robotics, and financial services.

The first European was the French explorer/trader Robert de La Salle in his 1669 expedition down the Ohio River from Lake Ontario and Quebec. This discovery was followed by European pioneers, primarily French, in the early 18th century. Michael Bezallion was the first to describe the forks of the Ohio in a manuscript in 1717, and later that year European traders established posts and settlements in the area. During 1753–54, the British hastily built Fort Prince George, but a larger French expedition forced them to evacuate and the expedition then proceeded to construct Fort Duquesne on the site. After the French abandoned and destroyed Fort Duquesne in 1758, Forbes ordered the construction of Fort Pitt, named after British Secretary of State William Pitt the Elder. He also named the settlement between the rivers "Pittsborough”. In 1784, the laying out of the "Town of Pittsburgh" was completed by Thomas Viceroy of Bedford County and approved by the attorney of the Penns in Philadelphia. In 1785 Pittsburgh became a possession of the state of Pennsylvania.

The area was officially called Pittsburgh in 1758 by General Forbes, and Fort Pitt was constructed in 1759.
There's an in-depth timeline here: http://digital.library.pitt.edu/cgi-bin/chronology/chronology_driver.pl?searchtype=dbrowse&year=1780&year2=1789&start_line=0
It depends when a city is considered "founded." There were lots of territoriality disputes regarding Pittsburgh, so your best bet is to take a look at the timeline for the exact information you're looking for specifically.