In Webstorm 8, it is not possible to apply regular expression filters on Grunt console output.
The way to go, as mentioned by lena, is to call Grunt directly via an External tool entry, and set up appropriate regex filters, such as:
For grunt-ts:
$FILE_PATH$\($LINE$,$COLUMN$\):.*
For grunt-tslint:
...$FILE_PATH$\[$LINE$,\s$COLUMN$\]:.*
Also see my comment above regarding a caveat for grunt-tslint in some environments.