The two clubs were paired together when the draw was made this morning in Switzerland.
The first leg will be at Parkhead in February with the second leg in Turin in March.
The Juventus team boasts Italian midfielder Andrea Pirlo and keeper Gianluigi Buffon.
Juventus, coached by Antonio Conte, were winners of the competition’s forerunner, the European Cup, in 1985 and 1996.
However, the Serie A champions snuck into the last 16 only by winning their final group game and will be expected to step it up when the competition resumes.
Their star player is Chilean Arturo Vidal, who joined Juventus from Bayer Leverkusen in 2011. The 25-year-old defensive midfielder has been nicknamed Il Guerriero (The Warrior) by the Italian press for his hard tackling and tenacious playing style.
Celtic boss Neil Lennon called his side's draw against Juventus "a beauty" but very tough.
Lennon said: "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 very tough, but it could have been any of the other teams and it would have been just as tough.
"We will take it as it comes, we're looking forward to the games now and I'm sure our supporters will be as well.
"We believe over two games anything is possible. Juventus are littered with world-class stars and have been very consistent over the last 18 months and have got a great winning mentality, but so have we.
"To come through the group as impressively as we did, you just never know where you'll be in a month or two's time in terms of fitness and form."
Reacting to the draw on Twitter, Celtic's Beram Kayal tweeted: "A special moment for the players watching the draw and everyone was excited."
The two other British survivors, Manchester United and Arsenal, will face Real Madrid and Bayern Munich respectively.
The first content will see Cristiano Ronaldo returning to Old Trafford to face Manchester United and will also pit Jose Mourinho against Sir Alex Ferguson in the first knock-out round of Europe's top club competition.
Barcelona, who Celtic famously beat in the qualifiers to reach the last 16, will take on the other Italian giants, AC Milan.
Galatasaray v Schalke
Celtic v Juventus
Arsenal v Bayern Munich
Shakhtar Donetsk v Borussia Dortmund
AC Milan v Barcelona
Real Madrid v Manchester United
Valencia v Paris St Germain
Porto v Malaga