Some vendors in the centre of the capital Kampala said the Red Pepper sold out in minutes.
The newspaper, which specialises in sensational gossip and political scoops, was closed in November.
Eight of its editors and directors were charged with treason and defaming President Yoweri Museveni, his brother and the security minister.
But last week Museveni pardoned them, clearing the way for the paper’s return to the streets.
The presidency said the pardon followed a promise from the paper’s management to “become more professional”.
Arinaitwe Rugyendo, a co-founder of the Red Pepper, told AFP: “We are going to polish our style but we will not self-censor.”
He insisted the paper would continue to be “bolder than the rest”.
Best known as a scandal sheet exposing the sex lives of local celebrities and businesspeople, the Red Pepper has also cultivated a reputation as a media pioneer willing to publish stories of state corruption.
The paper has attracted criticism outside Uganda for identifying alleged homosexuals in the conservative country where prejudice against sexual minorities has deep roots.
“The Red Pepper divides opinion. There are very many people who don’t appreciate its style,” said Peter Mwesige, executive director of the Kampala-based African Centre for Media Excellence.
– Flashy stories, serious impact –
A 2017 report by Reporters Without Borders ranked Uganda ranked 112 out of 180 countries for media freedom.
“Beyond the flashier stories Red Pepper has contributed by widening the horizons of what the media can publicly carry. There are lots of stories that have entered the public domain because Red Pepper has published them,” said Mwesige.
“Stories on the military, the first family, and the ownership of property by public officials wouldn’t have been exposed if not for Red Pepper.”
Red Pepper has attracted criticism outside Uganda for identifying alleged homosexuals in the deeply conservative country
In central Kampala, people gathered round newsstands eager to read the front page editorial splash which declared “Our Story How Red Pepper ‘Died’ And Rose From The Grave After Two Months”.
A total of nine pages were dedicated to describing the editors’ experience, comparing the reopening to a Biblical resurrection.
“I’m happy it’s back,” said Patrick Higenyi, a 46-year-old civil servant. “I think they can talk the reality rather than deceiving the country.”
Following the November shutdown some Ugandans celebrated on social media accusing the tabloid of ruining their lives with its scurrilous stories.
But, said Mwesige, “To think you can sacrifice the freedom of Red Pepper but maintain media freedom is misguided.”
However, he was critical of the opaque, closed-door deal last week between Museveni and senior managers that paved the way for the Red Pepper’s return.
“If there is ever a case of a chilling effect on the media, this is it,” he warned.
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