The London-based side won the Premiership last season and finished third this season.
The Warriors have already announced details of a pre-season friendly against another Premiership side, Exeter Chiefs at Sandy Park on Saturday 31 August (kick-off 3pm).
Glasgow Warriors head coach Gregor Townsend said: "Harlequins are one of the top sides in England and only narrowly missed out on a place in the Premiership final, so it will be a good test for us ahead of the new season.
"Our pre-season preparation is crucial as we build-up to our first league game at the start of September and these two matches will give us some much needed game time to ensure we're sharp and ready for the new campaign."
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