The tie will also pit Jose Mourinho against Sir Alex Ferguson in the most mouthwatering tie of the first knock-out round of Europe's top club competition.
Emilio Butragueno, Real Madrid's director of institutional relations, said it would be a special match for Ronaldo - and for the two managers.
He said on www.uefa.com: "I am sure it will be a special game for him (Ronaldo). He's a great professional. I'm sure he's going to do his best to help us qualify. It's going to very, very special for him.
"It will be a thrilling experience for everyone.
"But we know it's going to be tough, Sir Alex Ferguson has been there over 25 years and he's a fantastic manager - he knows how to get the best out of his players and they have top players, but we are Real Madrid and we will try our best."
United's club secretary John Alexander hoped there was a lucky omen in the draw.
He told Sky Sports News: "Out of several standout ties, I think this is the one.
"It's the tie that everyone wanted to see - but that nobody wanted to see, they wanted to save it for later in the competition.
"One thing going in our favour is that our one victory over Real Madrid in this competition was in the year we won the final at Wembley [in 1968] so let's hope that is a lucky omen."
Watch: Huge match-ups headline CL draw... More Videos
Barcelona will take on familiar foes AC Milan with the first leg at the San Siro.
Their most recent encounter was in the quarter-finals last season, when Barca prevailed 3-1 on aggregate with Lionel Messi scoring twice in the second leg.
AC Milan sporting director Umberto Gandini told www.uefa.com: "Last season we faced them twice (the group stage and quarter-finals), this time only once fortunately. We are now used to playing in Catalonia.
"We face a perfect machine, even if they had more problems than usual this season in the group stage. Let's just hope we will qualify this time around.
"This is the highest hurdle we could face but if we manage to pass it we can go all the way."
Barca coach Tito Vilanova was on Thursday morning having cancer treatment on his parotid gland before undergoing six weeks of chemotherapy.
Gandini said in support: "We are all very close to Tito Vilanova and his family and we wish him all the best for his surgery.
"We hope he will be on the bench against us."
German champions Borussia Dortmund face a tricky clash with Shakhtar Donetsk while local rivals Schalke take on Galatasaray.
Big-spending Ligue 1 outfit Paris St Germain will fancy their chances of beating Valencia, whose form has been patchy this season, and Malaga, who are performing better in the La Liga, meet Portuguese champions Porto.
Bayern Munich take on Arsenal while Celtic meet Italian champions Juventus.
Bayern chairman Karl-Heinz Rummenigge said: "This is a draw that we can be happy with. We know Arsenal well, but we must not underestimate them.
"It's important that we try to get a good result in London and get a goal to send out a signal.
"We can make it - we will go into it as favourites."
Celtic boss Neil Lennon called his side's draw against Juve "a beauty" but very tough.
Lennon told Sky Sports News: "Well in terms of glamour it's a beauty. Juventus are one of the great traditional European teams. They're current Italian champions and finished the group stage very strongly.
"So in terms of glamour it's great, in terms of qualification it is going to be very tough, but it could have been any of the other teams and it would have been just as tough.
United defender Rio Ferdinand played in the 2003 match against Real Madrid, as did Ryan Giggs, while Darren Fletcher was a substitute although he did not come on.
Ferdinand welcomed the draw on Twitter saying: "Oh yes, Madrid!! What a great couple a games that'll be!! @Cristiano see u soon bro!!"
United will play the first leg at the Bernabeu on February 13 with the return at Old Trafford on March 5.
Arsenal will play a week later with the first leg at the Emirates Stadium on February 19 and the second at the Allianz Arena in Munich on March 13.
Celtic will take on Juventus at Celtic Park on February 12, with the return leg in Turin on March 6.
Champions League last-16 draw
Galatasaray vs FC Schalke
Celtic vs Juventus
Arsenal vs Bayern Munich
Shakhtar Donetsk vs Borussia Dortmund
AC Milan vs Barcelona
Real Madrid vs Manchester United
Valencia vs Paris St Germain
Porto vs Malaga