It follows two near misses the two previous years when the authority won Silver Gilt Flora awards. Earlier shows helped them to silver or bronze gongs.
Andrew Carter, leader of Leeds City Council, said: "This is a day we have all dreamed of since Leeds first started coming to Chelsea," 13 years ago.
The HESCO Garden 2010 was the largest and most ambitious design entered by Leeds at Chelsea and was modelled on a section of the Leeds-to-Liverpool Canal, he said.
Canal and full-sized lock gates formed the centrepiece, described by RHS organisers as the first time such a water feature had appeared at Chelsea.
The garden celebrates green links connecting the city centre to the countryside and the canal and lock gates symbolise the industrial past of the city.
Woodland, wetland and a floral-meadow planting flank the lock gates, examples of which can be found in green spaces in Leeds.
Leeds' executive member for leisure John Procter said: "This gold medal award is the result of a massive collective team effort going right back to the first garden in 1997."
HESCO Bastion, a local engineering manufacturer, sponsored the garden, used by primary school kids in education projects.
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