Mr Romney said he had decided it was "best to give other leaders in the party the opportunity to become our next nominee".
His statement comes weeks after a surprise announcement saying he was considering another bid.
The decision not to run frees up donors to support other Republican candidates.
Mr Mitt Romney's campaign raised more than $1bn (£666m) in the 2012 election, when he unsuccessfully challenged President Obama.
Romney also lost the 2008 Republican presidential nomination to Senator John McCain.
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