The 22-year-old defender has joined the Blues on a four-year deal for a fee believed to be in the region of £6million.
Kompany became one of the most highly-rated young defenders in Europe after coming through the ranks at Anderlecht and representing his country at various youth levels.
Hamburg won the race to sign the cultured defender in 2006 to replace Daniel van Buyten, a fellow Belgian who had a successful loan spell at City in 2004.
Kompany has gone on to make 28 appearances for the German Bundesliga side and has won 23 caps for Belgium, recently appearing at the Olympics in Beijing.
He becomes City's 3rd signing of the summer after Jo and Tal Ben Haim, and can also play as a defensive midfielder, although surely the priority now for manager Mark Hughes must be to get another striker in before the transfer window slams shut.