Ronnie Kerr, wife Jannette and daughters Elizabeth, 8, and Joanna, 7, were greeted by city council leader Gordon Matheson, who told them they were the 500,000th visitors.
Bosses of the transport museum expected it would attract around 800,000 people in its first year.
But the stunning attraction on the banks of the Clyde has reached the half million mark in just seven weeks.
Since it opened, around 10,000 visitors every day have enjoyed the 3000 exhibits and 150 interactive displays telling the stories of the people behind the term "Clyde Built".
The museum's busiest day so far was June 25 – four days after it opened – when it attracted 15,000 people.
The Kerrs, who live in Aberdour, Fife, were presented with goodie bags and lunch at the Riverside Cafe to mark the special occasion.
Mr Kerr said: "My dad worked in the yards at Yarrow's and I would have loved to have shown him round the museum.
"It is a fantastic building and they have done a great job.
"I had been to the previous transport museums at Kelvin Hall and Albert Drive, but this building is something else and we really enjoyed our visit."
Mr Matheson said Riverside had been a huge hit.
He added: "We knew just how much visitors loved the Museum Of Transport at the Kelvin Hall but, even so, the reaction to the Riverside Museum has been phenomenal.
"The feedback from people has been overwhelmingly positive and we are already seeing visitors returning time and again to enjoy Glasgow's latest attraction."
However, some visitors have complained about being unable to find a space in the museum's car park.
A spokesman for Glasgow Life, which runs Riverside, said: "Even with 100 more spaces than Kelvingrove, the car park has often been full, but alternative parking is available at Kelvin Hall and Kelvingrove Art Gallery and Museum, which are both a short walk from the Riverside Museum.
"The museum is well served by public transport, including a new dedicated bus service from George Square (service 100).
"There is also the reinstated ferry from Govan, which links the Subway and bus routes, or you can make the short walk from Partick Interchange in less than 10 minutes."
Parking at Riverside is £1 for three hours and £1 for four hours at Kelvin Hall.
Highlights at the museum include the wall of cars, the hanging bicycle velodrome, the massive South African locomotive, the motorbike deck, the Rest And Be Thankful display, the recreated street from the 1900s and the 1930-80s areas.
Other attractions include hand-made bikes belonging to Scot Graeme Obree, the former world cycling champion, and the Subaru Impreze that Colin McRae drove to win the World Rally Car Championship.