Gary Gowans' short film shows the Millennium Falcon emerging from the building, chased by Imperial TIE fighters, as R2-D2 looks on.
The film fades to black as the V&A logo expands to become "Vader", with the sound of Darth Vader's breathing.
Mr Gowans, from Newport-on-Tay, said he made the film to "cheer himself up" after a bout of flu.
The short film has been viewed more than 203,000 times on Facebook since being posted on Sunday.
The Â£80.1m museum is currently under construction and is due to open in summer 2018.
V&A Dundee said it was "delighted" that it had inspired the video.
Mr Gowans, who is a senior lecturer in graphic design at Dundee's Duncan of Jordanstone art college, said:  "I drive past it every day, it's a beautiful building.
"The look of it at the moment feels a little Star Wars-y.
"Every time I drive by it I can't get Darth Vader's death march tune out of my head.
"When I go past it I just hear Star Wars theme tunes.
"I did it over a couple of weekends and a few nights here and there. I thought I'd have a bit of fun and post it to a few friends."
Mr Gowans said he was "slightly shell-shocked" at the reaction to the video.
He said: "It's the first time I've ever done anything on Facebook.
"I posted it at four o'clock and I thought a few folk would see it.
"I woke up this morning and my daughter and my wife said you won't believe the amount of people who are viewing it.
"It's all a bit of a surprise."
A V&A Dundee spokesman said: "We're delighted to see talented people like Gary being inspired by our building before we even open next year, resulting in such fun and creative work."
A filmmaker's reimagining of Dundee's new V&A Museum as a Star Wars space port has become an internet hit.