UN officials have been warning for years that the Red Sea and Yemen's coastline was at risk as the Safer tanker could spill four times as much oil as the 1989 Exxon Valdez disaster off Alaska.
A UN spokesperson said on Tuesday a spill could cost US$20 billion to clean up.
The war in Yemen caused the suspension in 2015 of maintenance operations on the Safer, which is used for storage and has been moored off Yemen for more than 30 years.
The UN, which has never before undertaken such a rescue mission, has warned its structural integrity has significantly deteriorated and it is at risk of exploding.
"In the absence of anyone else willing or able to perform this task, the United Nations stepped up and assumed the risk to conduct this very delicate operation," UN Secretary-General Antonio Guterres said.
"The ship-to-ship transfer of oil which has started today is the critical next step in avoiding an environmental and humanitarian catastrophe on a colossal scale."
The oil transfer is expected to take 19 days to complete, the United Nations' Development Program (UNDP) said in a statement.
"We are obviously very cautious – it's only the beginning of a transfer," UNDP spokesperson Sarah Bel told a Geneva press briefing when asked about the operation's risks.
"The cost of an oil spill is estimated to be approximately US$20 billion, and it will take years to clean up," she added.
She warned that any spilled oil could reach the African coast, damaging fish stocks for the next 25 years and destroying 200,000 jobs.
It would also close ports that bring food and supplies to Yemen, where some 17 million people rely on humanitarian aid, she said.
