Clubs cannot face an opponent from their own country or qualifying group.
Defending European champion Madrid were perhaps most impressive in the group stage with a perfect record, contributing six of the club's current Spanish record streak of 20 straight wins.
Madrid advanced with two matches to spare and their 11-point lead over runner-up Basel was a competition record.
Cristiano Ronaldo, who scored a Champions League-record 17 goals last season, has five so far, allowing Lionel Messi to build a 75-72 lead in their ongoing duel for the all-time competition scoring record.
In a season of heavy scoring and lopsided wins, even Messi's eight goals for Barcelona does not top the standings.
Shakhtar forward Luiz Adriano has nine - matching Ronaldo's group-stage record last season - with eight scored against BATE Borisov of Belarus.
The Ukraine champion's 7-0 and 5-0 routs of BATE were among 15 matches in the group stage won by at least four goals. There were just 16 such wins in the past two group phases combined.
Also, half the teams in today's draw racked up double-figure goal difference in the groups.
Monaco bucked that trend, scoring only four in six matches after letting star Colombian forwards James Rodriguez and Radamel Falcao leave in the summer.
A pairing with Monaco would send Arsenal coach Arsene Wenger back to where he made his reputation in the 1980s. It would also be rare good Champions League fortune for Arsenal, who recently exited the last-16 stage against Barcelona and Bayern.
Dortmund are the most unpredictable seed with the 2013 runner-up shining in the Champions League while spending much of the season near the bottom of the Bundesliga.
PSG, who were runner-up in Barcelona's group, could be the toughest unseeded option, though English champion Manchester City have momentum from their unlikely turnaround sparked by Sergio Aguero's hat-trick to defeat Bayern last month.
Ten of the 16 teams come from three nations - Spain, England and Germany - and only one is from eastern Europe.
However, Shakhtar play closer to the west than they would choose. Donetsk is the centre of conflict with pro-Russian separatists, so Shakhtar plays "home" matches in Lviv, near Ukraine's border with Poland.
The final is played on June 6 at the Olympic Stadium in Berlin.
Champions League
*Seeded teams: Atletico Madrid (Spain), Real Madrid (Spain), Monaco (France), Borussia Dortmund (Germany), Bayern Munich (Germany), Barcelona (Spain), Chelsea (England), Porto (Portugal).
*Unseeded teams: Juventus (Italy), Basel (Switzerland), Bayer Leverkusen (Germany), Arsenal (England), Manchester City (England), Paris Saint-Germain (France), Schalke (Germany), Shakhtar Donetsk (Ukraine).
- AP
