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The Giallorossi will face Sergio Conceicao's side in the New Year, with the first leg taking place at the Stadio Olimpico on Tuesday February 12.
The second leg, at the Estadio do Dragao, takes place on Wednesday March 6.
Porto topped a group that included Schalke 04, Galatasaray and Lokomotiv Moscow to be seeded in the draw for the knockout phase.
Roma - semi-finalists in the competition last season - finished second in their group behind Real Madrid to reach this stage.
“Perhaps we can say we are a bit fortunate [with this draw], looking at some of the other sides we could have faced,” club director Francesco Totti said.
“But Porto are a great side, in good form, they are top of their league and just completed a very strong group stage in this competition. They will be a very tough opponent. We will have to be at our best from the first moment.”
He added: “We want to repeat what we did last season in the Champions League, even though obviously we know that will be far from easy. We haven’t been great in the league so far this season, but we still have a chance to rebound and do much, much better than we have been doing.
“We’ve got two months until the game arrives. We will try to be back to our very best by the time the tie comes around. We need to find consistency and results and bring back a bit of confidence to the players and the staff, everyone.”
The two sides last met in European competition back in 2016, in the final play-off round to qualify for the Champions League group stage.
On that occasion Porto emerged victorious, winning 4-1 on aggregate.
"The draw could have been worse, but Porto knocked us out of this competition barely two years ago,” managing director Mauro Baldissoni said.
“We need to get back to being the real Roma, if we want to be able to compete against these sides. The squad has talent, but hasn’t shown it consistently this season.”
Elsewhere there were some mouth-watering ties - with Bayern Munich facing Liverpool and Manchester United facing Paris Saint-Germain.
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