Mr Obama was awarded the title "for having the confidence to sketch an ambitious future in a gloomy hour," said the US-based magazine.
It said he showed "the competence that makes Americans hopeful he might pull it off".
Recent winners have included Russian Prime Minister Vladimir Putin, the American soldier and the online public.
Time told readers it was "unlikely that you were surprised to see Mr Obama's face on the cover".
I hope Time named Obama because he inspired thousands to take back responsibility in deciding who will run America
"He has come to dominate the public sphere so completely that it beggars belief to recall that half the people in America had never heard of him two years ago.
"He hit the American scene like a thunderclap, upended our politics, shattered decades of conventional wisdom and overcame centuries of the social pecking order."
Mr Obama has featured on the magazine's cover 15 times in the past two years.
"We would have had to have had some pretty compelling reasons to not chose President-elect Barack Obama," Michael Elliot, Time's international editor, told CNN.
"His is an extraordinary story which has captured the imagination of people from Jakarta to Dublin to Iowa to New Hampshire.
"There is a degree of excitement surrounding Barack Obama which we tried to capture in our choice," Mr Elliot said.
Time began selecting a "Man of the Year" in 1927 and has selected a man, woman or group every year since. In one year it chose the computer for the title.
TIME'S 'PERSON OF THE YEAR'
Time says its award recognises 'the most powerful individuals and forces shaping the world'
Many US presidents have been named Person of the Year, including George W Bush and Bill Clinton
Controversially, Adolf Hitler, Joseph Stalin and Ayatollah Khomeini have also been given the title
In 2006, the magazine gave the award to everyone who had used or created online content that year
In 1999, the title was changed to "Person of the Year" to be more inclusive.
The BBC's Andy Gallacher in Washington says receiving the accolade is usually considered an honour.
But is has also been awarded to Adolf Hitler and Joseph Stalin in the past, for less honourable reasons.
Four runners-up for this year's title were also announced, as well as 17 "people who mattered".
The runners-up were US Secretary of the Treasury Henry Paulson, French and current EU President Nicholas Sarkozy, Republican vice-presidential candidate and Alaskan governor Sarah Palin and Zhang Yimou, creative director of August's Olympic opening ceremony in Beijing.
Among the "people who mattered" were released Colombian hostage Ingrid Betancourt, Zimbabwe's President Robert Mugabe, the former CEO of the collapsed bank Lehman Brothers and Tina Fey, the actress who impersonated Mrs Palin during the US election campaign.