The way to do it is to use the Tabulate Area tool:
Spatial Analyst Tools --> Zonal --> Tabulate Area
The output is the cross-tabulted areas between 2 rasters.
Give the first raster as the input raster or feature zone raster, the zone field is the land cover class field, the second raster is your second input raster.
The result will be in areas not in amount of cells, but to arrive to the number of cells, you just need to divide it by your raster resolution (e.g, if the raster is 1kmx1km, divide the output by the resoltion in meters: 1000x1000)
The vertical will be your first raster cell values (FROM), the horizontal your second raster cells values (TO).