Hosts Russia, defending champions Germany and 30 other teams will discover their opponents for the 21st World Cup, due to be played in 11 cities and 12 stadiums from June 14-July 15.
Russia will kick off the tournament on June 14 at Moscow's Luzhniki Stadium, which is also the venue for the final.
The draw comes as Russia faces a potential ban at the 2018 Winter Olympics in Pyeongchang over doping, following the exclusion of its track and field athletes at the 2016 Rio Games.
It will also be the first World Cup tournament under new leadership at world governing body FIFA after the corruption scandals which led to football bans for leading officials including former president Joseph Blatter.
Putin now welcomes to the Kremlin new FIFA president Gianni Infantino, who along with 30 of the 32 national team coaches present, will see a 60-minute star-studded show.
Former England striker Gary Lineker is co-hosting the draw with Russian sports journalist Maria Komandnaya and will be assisted by a host of former greats including Argentina's Diego Maradona, ex-England goalkeeper Gordan Banks and 91-year-old Russian Nikita Simonyan.
Local television personality Ivan Urgant will host the full show, with musical performances by Russian pop star Alsou, opera singer Ildar Abdrazakov and actress Larisa Dolina.