The 25-year-old, who has been at Griffin Park since June 2011, arrives at Pittodrie in a loan deal for the remainder of the campaign.
Logan has previously played with Dons striker Niall McGinn, who moved to Aberdeen two months after a season on loan with the west London club.
Aberdeen boss Derek McInnes may hand Logan his debut in Saturday's League Cup semi-final against St Johnston at Tynecastle.
Meanwhile, the Dons have loaned striker Josh Magennis to Scottish Premiership rivals St Mirren until the end of the season.
The Northern Irishman has only scored once this season in 20 appearances for Aberdeen, when he netted in the 3-0 victory at Partick in September.
St Mirren boss Danny Lennon is looking to refresh his squad in an attempt to move clear of the relegation play-off position in the league.
And Lennon is hoping to add at least one more player before the transfer window closes on Friday night.