Celtic were in the Champions section of the draw and will be at home in the first leg with Finnish title-holders HJK very likely to be their opponents after they won the first leg of their second qualifying round clash with KR 7-0 earlier this week.
Motherwell were unseeded in the draw and will face a stiff test against 20-time Greek champions Panathinaikos, with the first leg taking place at Fir Park.
The first legs will be played across July 31 and August 1, with the return legs contested a week later.
Celtic boss Neil Lennon and captain Scott Brown have already targeted reaching the group stages of the tournament with others suggesting it is a necessity given the lack of Old Firm matches for the foreseeable future.
Motherwell's Champions League opportunity stemmed from the demise of oldco Rangers and the rejection of Charles Green's newco club into the SPL but Stuart McCall's side will go into their clash as underdogs.
However Celtic should also be wary of their likely opponents with HJK Helsinki taking apart Icelandic champions KR with ease on Tuesday evening.
The Hoops faced Helsinki in the first round of the UEFA Cup in 2000, with a goal in extra-time from Chris Sutton earning Martin O'Neill's side a 3-2 aggregate win.