Owner Chris Clarkson drove the Tesla Model S P85+ into the Glasgow Museums Resource Centre in Nitshill.
The four-year old car, which cost Â£107,000 new, will go on display at the centre before being transferred to the Riverside Museum next year.
It will give many people their first chance at a Scottish museum to see at close quarters a car that helped revolutionise electric motoring.
Staff are considering how visitors can interact with some of the car's technology, which include a car-shaped key fob that opens doors and the boot by pressing the relevant part.
Still worth some Â£40,000, the Tesla will form part of a display about engineering ingenuity to mark the bicentenary of Greenock-born inventor James Watt.
Mr Clarkson, from Strathaven in South Lanarkshire, is donating what was his company car following the sale of his online travel business.
He said he had been one of only a handful of Scottish Tesla owners in 2014.
Mr Clarkson said: "My family have really enjoyed our time with this incredible machine and it’s exciting to see a car of the future now take up its place in history."
Glasgow Museums transport curator Neil Johnson-Symington told The Scotsman: "It's an absolutely amazing gift opportunity.
"It represents so much in terms of cutting-edge design, pioneering technology and environmental awareness.
"It could not have come at a better time with the Scottish Government announcing it is planning to phase out petrol and diesel cars by 2032."
On plans to showcase the car, he said: "We want the public to see its bells and whistles and need to think how they will be able to experience it."
David McDonald, chair of city council firm Glasgow Life, which runs the museums, said: "This car is a very special object.
"It is a pioneer representing a new dawn in electric vehicle development."
Motoring writers have called it a "game changer" and the most important car of the last two decades.
It can travel 242 miles on a single charge at a cost of about Â£9 and can reach 0-60mph in four seconds.
Tesla had added a service centre at Newbridge in Edinburgh after opening its first Scottish showroom in Multrees Walk, off St Andrew Square, at the end of 2015.
The firm declined to say whether it is progressing plans for a showroom in Glasgow.
The Tesla will join a Honda Insight, an early hybrid car from 2000, which was given to the Riverside Museum two years ago.