I have a shapefile. The coordinates (Lat/Long) are projected as meter (555000, 155000). But, I want to re-project it to decimal degrees(51.523666, -0.07467).
How can I do it with QGIS?
In QGIS, it's very straightforward. First, ensure that you have the correct coordinate system for your original shapefile:
It's a very good idea to make sure you select a good name in the "Save as" dialog - appending the coordinate system to the name can be very helpful, e.g. my_shape_file_DD_WGS84 to remember that it's in degrees, WGS84.
I would just add as a step 3:
3) Once the layer is re-projected in WGS84 ESPG:4326, go to Vector > Geometry Tools > Add Geometry Attributes (Calculate Using Layer CRS)