Grace will make his Crucible debut against world No 14 Kyren Wilson with a meeting against Stuart Bingham or Peter Ebdon, both former world champions, in the second round.
The 31-year-old, ranked 51 in the world, reached snooker’s biggest stage for the first time after beating Thailand’s Akani Songsermsawad 10-3 in the final round of qualifying.
Chinese star Ding Junhui, seeded fourth, has been paired with compatriot and fellow Sheffield-based player Zhou Yuelong, who is making his Crucible bow.
Teenage sensation Yan Bingtao, who trains alongside Ding and Zhou in the Steel City, will become the first player born in the 21st century to play at the Championships when he meets 2005 world champion Shaun Murphy.
Defending champion Mark Selby will meet Fergal O'Brien in the opening round after the Irish qualifier played out the longest frame in snooker history to book his place in the draw.
First round draw
Mark Selby v Fergal O'Brien
Ryan Day v Xiao Guodong
Neil Robertson v Noppon Saengkham
Marco Fu v Luca Brecel
Shaun Murphy v Yan Bingtao
Ronnie O'Sullivan v Gary Wilson
Liang Wenbo v Stuart Carrington
Ding Junhui v Zhou Yuelong
Stuart Bingham v Peter Ebdon
Kyren Wilson v David Grace
Mark Allen v Jimmy Robertson
John Higgins v Martin Gould
Barry Hawkins v Tom Ford
Ali Carter v Graeme Dott
Anthony McGill v Stephen Maguire
Judd Trump v Rory McLeod