Dundee Heritage Trust launched the campaign to pay for initial restoration and preservation work to the ship's masts and rigging.
More than 200 backers contributed to the crowdfunding campaign.
The nine-month repair programme, which began in November at Discovery Point, will cost £350,000.
The masts and rigging were removed and have been sent to a specialist shipbuilders in Gloucester for repair.
RRS Discovery was built in Dundee in 1900 for Captain Robert Falcon Scott's first Antarctic expedition. It was returned to the city in 1986.
Dundee Heritage Trust executive director Paul Jennings praised "amazing" public support for the campaign.
He said: "Not only does it enable us to carry out this important restoration work on the ship, but it proves how dear RRS Discovery is to people, particularly in her home city."
Television presenter Lorraine Kelly, who launched the crowdfunding campaign with a video appeal, said:  "It's been so gratifying to see people get behind this campaign to help preserve one of the country's, and in particular Dundee's, most important visitor attractions.
"It was a pleasure to front this crowdfunding effort and to see the public and businesses really step up to help."
A £40,000 crowdfunding campaign to help restore Captain Robert Falcon Scott's expedition ship RRS Discovery has hit its target.