Sea level rises as a result of global warming for two reasons:
The chart below shows the historic sea level rise, as calculated by satellite sea level calculations produced by the NASA Goddard Space Flight Center. Based on this data, NASA estimate sea level is rising by 3.4mm per annum at current rates of warming.
Historic sea level measurements
Data shows that melting ice from the Greenland ice cap is the largest contributor to sea level rises. In addition to melting of the Greenland and Antartic ice sheets, smaller ice caps and glaciers around the world are showing signs of accelerated retreat, also contributing to sea level changes.
The video below shows historic changes in Arctic sea ice
Understanding the sea level changes that are attributable to global warming is not straightforward - various other naturally occurring factors can contribute to sea level changes which need to be considered as part of any measurements:
NASA has more information at this link.