The 115-year-old Antarctic exploration vessel created a huge buzz in the city when she arrived from London in 1986.
Now, the ship is expected to get another boost by being docked yards away from the £80 million V&A Dundee museum, which is due to open in 2018.
Thousands of people turned out to greet her arrival, which was seen as marking a turning point in the city’s fortunes after years of decline.
Lord Provost Bob Duncan said the ship “has been central to the setting of a new course for Dundee”. The city’s slogan is “City of Discovery”.
The 172ft-long Discovery was the last traditional three-masted wooden ship to be built in Britain.
She was constructed by Dundee Shipbuilders Company at a cost of £51,000 - around £4.1 million today.
Past visitors have included the Duke and Duchess of Cambridge, who toured the ship during a visit to Dundee last October.
Her missions have included carrying the 1901 British National Antarctic Expedition, in which Robert Falcon Scott and Ernest Shackleton made their first successful journey to the Antarctic.
Professor Stewart Brymer, who helped bring Discovery back to Dundee, remembers her return.
He told the BBC: “We can all remember when Discovery sailed back up the river.
“The image that then gave to Dundee, the City of Discovery, has been no mean feat.
“It was a wonderful day. But if we look back on that day, we can see the return of Discovery actually igniting a spirit within the people of Dundee.
“The people got behind Discovery coming back to the city where she was constructed and launched in 1901.”
Gill Poulter, of Dundee Heritage Trust, which owns the ship, said: “Discovery is really important to Dundee’s history and heritage.
“Obviously, people associate her with Scott of the Antarctic and that British National Antarctic exhibition.
“But for local people,, she’s a proud reminder of the city’s shipbuilding past and whaling heritage.
“Undoubtedly, Discovery was important for regenerating the city and turning perceptions of the city around, so it could be seen as a tourist attraction.”
After the 1901 expedition, financial problems led to Discovery being sold to the Hudson’s Bay Company in Canada four years later, where she became a transatlantic cargo vessel.
Discovery saw service in the First World War transporting munitions to Russia.
In 1923, she returned to research work in the Antarctic and was designated as a RRS.
She became a training ship for the Scouts in 1936, with her engines and boilers removed as scrap to help the war effort.
Her condition deteriorated until she was on the verge of being scrapped, with The Maritime Trust stepping in to save her from the breakers’ yard in 1979.
She spent time berthed on the River Thames, eventually reverting to the RRS designation and opening as a museum.
Discovery was passed into the ownership of the Dundee Heritage Trust in 1985, following a £500,000 restoration carried out by The Maritime Trust.
The vessel left London in March 1986, on board cargo ship Happy Mariner, to make her trip home to the city that built her.
She arrived on 3 April and was eventually moved to a custom-built dock in 1992.