Williams, 42, was forced to qualify after he was defeated by Mark Selby on Sunday in the final of the China Open.
He will be one of 14 Welsh players who will have to win three qualifying rounds at Ponds Forge in Sheffield to secure a place in the first round.
Ryan Day is the only Welshman to be guaranteed a place in the competition.
The World Championship starts at Sheffield's Crucible Theatre on Saturday, 15 April.
15-year-old schoolboy Jackson Page and amateur Tyler Rees, 18, will play in the qualifying rounds after receiving an invitation to compete.
Page, of Ebbw Vale, will take on world number 75 Martin O'Donnell on Thursday while Rees will play against world number 44 Xiao Guodong of China on Wednesday.
Elsewhere, Matthew Stevens - twice a runner up at the Crucible - will face off against fellow Welshman Lee Walker on Wednesday.
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Two-time world champion Mark Williams will face China's world number 84 Zhao Xintong in the World Championship first qualifying round on Saturday.