Several Democrats gave their support, for a total of 72 of 100 senators casting their votes for the 79-year-old billionaire who specializes in troubled businesses and is now tasked with implementing Trump's promises to return industrial jobs to the United States.
A total of 21 Democrats voted for him.
Ross, who succeeds another billionaire, Penny Pritzker, will now also coordinate US commerce policies with the US trade representative, a post for which Trump has nominated Robert Lighthizer, who awaits Senate confirmation.
Democrats' questions of Ross's ties with Russia come at a time when Trump is defending his administration's relations with Moscow, following leaks about repeated contacts between members of his campaign team last year and Russian intelligence officials.
Since 2014, Ross has served as vice chairman of the Board of Directors of the Bank of Cyprus, the largest bank in Cyprus, which was saved from bankruptcy in 2013 by a bailout from the Eurozone countries and the IMF and by forced contributions from most of its savers.
This bank also is the second largest shareholder in the Russian conglomerate Lamesa Holding, owned by the Russian oligarch Viktor Vekselberg, whose fortune is valued at more than $12 billion by Forbes.
"@CommerceGov nominee Wilbur Ross is practically a cartoon stereotype of a Wall Street fat cat with no interest in anyone but himself," wrote prominent Trump opponent Senator Elizabeth Warren.
Ross's predecessor as vice chairman of bank's board is Vladimir Strzhalkovsky, a former KGB agent known to be close to Russian President Vladimir Putin.
"The United States Senate and the American public deserve to know the full extent of your connections with Russia and your knowledge of any ties between the Trump Administration, Trump Campaign, or Trump Organization and the Bank of Cyprus," Democratic Senator Cory Booker said in a letter to Ross.
In mid-February, Booker and five other Democratic senators sent a letter to Ross asking him whether the Bank of Cyprus had lent to Trump's real estate group, the Trump Organization.
The officials also called on Ross to reveal whether he had any contact with Russian officials or agents during the presidential campaign.
Ross's team did not immediately respond to a request for comment.
Senate Democratic Minority Leader Chuck Schumer deplored the fact that the White House would not release Ross's response to the Democrats' queries.
"It is another example of this administration abandoning transparency and trying to jam their nominees through without making all the relevant information public and available," Schumer said on the Senate floor.
"On an issue as sensitive and important to national security as Russia, it is another black mark on this nascent administration."
In mid-February, Trump's national security adviser, Michael Flynn, was forced to resign after it was revealed that he misled Vice President Mike Pence and other administration officials about pre-inauguration discussions he had with the Russian ambassador in Washington about US sanctions against Russia.
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