GRASS will be very helpful to you since it uses a computational region to work on :

In computations,

 

• raster input maps are automatically cropped/padded and rescaled (using nearest neighbour resampling) to match the current region in order to produce the output raster map or to query values.

 
• Raster output maps have their bounds and resolution equal to those of the current computational region.

 
• Vector maps are always considered completely.

So, using GRASS, you will define the region according to the existing raster

   g.region rast=myExistingRaster

(Adding -p option to the command will display raster properties)

And then, run the command to rasterize your vector layer :

   v.to.rast

More info on v.to.rast command is available online.

GRASS will be very helpful to you since it uses a computational region to work on :

In computations,

• raster input maps are automatically cropped/padded and rescaled (using nearest neighbour resampling) to match the current region in order to produce the output raster map or to query values.

• Raster output maps have their bounds and resolution equal to those of the current computational region.

• Vector maps are always considered completely.

So, using GRASS, you will define the region according to the existing raster

   g.region rast=myExistingRaster

(Adding -p option to the command will display raster properties)

And then, run the command to rasterize your vector layer :

   v.to.rast

More info on v.to.rast command is available online.