Yes, this is Archimedes' principle. However, large icebergs have a gravitational influence on nearby water. Effectively, large icebergs attract water meaning the local sea level rises and elsewhere on the planet the sea level becomes lower. When the iceberg melts, this gravitational pull disappears and the melt water is spread more evenly across the surface of the Earth. The sea level across the rest of the world thus slightly increases.
Modeling this effect is quite complex, but the above is a summary of the effect of melting (large) icebergs.