The Magpies, in the group stage for the first time since 2002-03, face three sides who have all at least reached the final in the past 16 years.
Arsenal have been paired with Sevilla and Celtic face Atletico Madrid.
Group stage draw in full
Group A: Bayern Munich, MANCHESTER UNITED, FC Copenhagen, Galatasaray
Group B: Sevilla, ARSENAL, PSV Eindhoven, RC Lens
Group D: Benfica, Inter Milan, Salzburg, Real Sociedad
Group E: Feyenoord, Atletico Madrid, Lazio, CELTIC
Group F: Paris St-Germain, Borussia Dortmund, AC Milan, NEWCASTLE
Group G: MANCHESTER CITY, RB Leipzig, Red Star Belgrade, Young Boys
Group H: Barcelona, Porto, Shakhtar Donetsk, Royal Antwerp
The group stages will run from 19 September to 13 December, with the final at Wembley on 1 June.
Magpies face daunting return to Champions League
Newcastle's long-awaited return to Europe's elite competition has been much anticipated after they finished fourth in the Premier League last season - but their draw could barely have been more difficult.
Eddie Howe's side will play PSG, who reached the final in 2020, and seven-time European champions and last season's semi-finalists AC Milan in Group F.
They will also play Borussia Dortmund, who won the competition in 1997 and most recently reached the final 10 years ago.
The Gunners, also back in the competition for the first time since 2016-17, will face PSV Eindhoven and French club RC Lens, along with Europa League winners Sevilla in Group B.
Manchester City's draw looks relatively kind by contrast, with RB Leipzig, Swiss side Young Boys and Red Star Belgrade, who won the European Cup in 1991, joining them in Group G.
Manchester United have been drawn against German champions Bayern Munich in a repeat of the 1999 final, with FC Copenhagen and Galatasaray also making up Group A.
Along with Atletico Madrid, Celtic will play Lazio and Dutch champions Feyenoord in Group E.
'Newcastle can look forward to some special nights on Tyneside'
BBC Sport's chief football writer Phil McNulty:
Newcastle United's return to the Champions League has given them arguably the toughest group to navigate towards the knockout phase after the draw in Monaco.
Paris St Germain, Borussia Dortmund and AC Milan await in Group F for Eddie Howe's side and, while this presents the toughest of tests, it also offers up the prospect of some truly special nights on Tyneside as Newcastle attempt to demonstrate their new ambitions against elite opposition.
The rest of the Premier League clubs will be cautiously optimistic of progress while Newcastle will hope a fevered atmosphere at St. James' Park will fuel their attempts to reach the last 16.
Manchester United will face England captain Harry Kane when they confront Bayern Munich but Copenhagen and Galatasaray offer a genuine opportunity for progress.
Arsenal will face European specialists and Europa League holders Sevilla but a group also containing PSV Eindhoven, convincing conquerors of Glasgow Rangers, and Lens should hold no terrors.
Holders Manchester City, meanwhile, will be overwhelming favourites to reach the last 16 and top their group, in which they will play RB Leipzig, Red Star Belgrade and Young Boys of Switzerland.