Thanks to @Daniel
I finally succeed integrating Git & my favorite comparison tool Devart CodeCompare
To integrate add the following lines to the c:\Users\[User Name]\.gitconfig file
[diff]
tool = codecompare
guitool = codecompare
[merge]
tool = codecompare
[mergetool]
keepBackup = false
[difftool "codecompare"]
cmd = 'C:/Program Files/Devart/Code Compare/CodeCompare.exe' \"$LOCAL\" \"$REMOTE\"
renames = true
[mergetool "codecompare"]
cmd = 'C:/Program Files/Devart/Code Compare/CodeMerge.exe' -MF=\"$LOCAL\" -TF=\"$REMOTE\" -BF=\"$BASE\" -RF=\"$MERGED\"
trustExitCode = true
Now git difftool will work properly from both command line and Git Extensions.
P.S. I strongly recommend to disable Visual Studio integration with CodeCompare during installation. I think it is much better to use its stand-alone host because of the performance.
EDIT: I found that mergetool was not working. Updated it.