Rugby league convert Burgess only made his union debut for Bath in November and won his first England cap against France in August.
The 26-year-old's inclusion means there is no place for fellow centre Luther Burrell, a regular during the past two Six Nations campaigns.
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Head coach Stuart Lancaster has also left out fly-half Danny Cipriani.
Cipriani's omission comes despite the 27-year-old Sale player putting in an impressive performance off the bench in the 25-20 defeat by France in Paris on Saturday, later tweeting he was "very disappointed" and had done "everything I could for the white shirt".
Exeter's Henry Slade, 22, is named as one of four centres alongside Burgess, Saracens' Brad Barritt and Jonathan Joseph of Bath, while Kieran Brookes is picked ahead of loose-head Alex Corbisiero, who has struggled with fitness recently.
Ben Morgan is named as one of the back rows, despite having played just 40 minutes of competitive rugby since suffering a broken leg and, in the second row, George Kruis has beaten Dave Attwood to a spot in the 31.
The other players to miss out are centre Billy Twelvetrees, number eight Nick Easter, flanker Calum Clark and hooker Luke Cowan-Dickie.
Head coach Lancaster, whose side begin their tournament against Fiji at Twickenham on 18 September, admitted to shedding tears over the selection of his squad.
He informed successful and unsuccessful players of his decisions in one-to-one meetings and when asked about the emotion of the talks, said: "Just by me. No tantrums, just tears."
He added "Selection wasn't easy and it is tough to leave anyone out but it's important to stress that the players not in this group are still part of our wider squad and could come in at any point.
"It's really positive that we have such depth and options to choose from.
"After 10 weeks in camp we have made our final selection of players and we believe we have a great group to take us into the tournament.
"With three weeks to go before we play Fiji we feel we are in good shape as we head into next Saturday's game against Ireland."
England backs coach Andy Farrell, who himself converted from rugby league to play in the 2007 World Cup with England, said of Burgess: "To force our hand to put him into the squad, he should be unbelievably proud of himself."
However, earlier this week, former England captain Will Carling said that Burgess should not be taken to the World Cup after frequently being caught out of position against France.
"There is no-one I have spoken to who I respect - ex-players, coaches - who thinks he's ready," said Carling, who won 72 caps for England and led them to the 1991 World Cup final.
"I don't understand what the rush is and it's unfair on him. I feel sorry for him. If he wants to make it in union, there's plenty of time.
"He's been playing union for 10 months and half of that was in a different position to what England are playing him in.
"I don't believe he's one of the four best centres in England."
When asked about the omission of Cipriani, who has been capped 14 times for England since making his debut in 2008, Lancaster explained he was edged out by specialist performers at both fly-half and full-back and rejected suggestions he had not had a chance to stake a claim.
"During training everyone has had plenty of opportunities to put their talent forward," he said.
"It's tough on Danny, he's a good player. We think he's improved but he's just lost out."
Cipriani accepted his non-selection, tweeting a long message that said he was grateful for the time he had been given to prove himself, emphasising the good communication he had enjoyed with the coaching staff.
While he understood the reasoning behind his exclusion, he added: "I would not be a true competitor if I said I agreed as we all believe in ourselves.
"But I had a long way to make up as the squad had been building since 2012... It's just the start of my journey. I am going to stay fit and be ready if I'm called upon."
He ended by urging everyone to support the squad. "Now that the call has been made let's just all get behind the team and back the 31."
Hookers: Jamie George (Saracens), Rob Webber (Bath), Tom Youngs (Leicester).
Props: Kieran Brookes (Northampton), Dan Cole (Leicester), Joe Marler (Harlequins), Mako Vunipola (Saracens), David Wilson (Bath).
Second rows: George Kruis (Saracens), Joe Launchbury (Wasps), Courtney Lawes (Northampton), Geoff Parling (Exeter).
Back rows: James Haskell (Wasps), Ben Morgan (Gloucester), Chris Robshaw (captain, Harlequins), Billy Vunipola (Saracens), Tom Wood (Northampton).
Scrum-halves: Danny Care (Harlequins), Richard Wigglesworth (Saracens), Ben Youngs (Leicester).
Fly-halves: Owen Farrell (Saracens), George Ford (Bath).
Centres: Brad Barritt (Saracens), Sam Burgess (Bath), Jonathan Joseph (Bath), Henry Slade (Exeter).
Back three: Mike Brown (Harlequins), Alex Goode (Saracens), Jonny May (Gloucester), Jack Nowell (Exeter), Anthony Watson (Bath).
BBC Radio 5 live's Rugby World Cup preview show takes place at the Twickenham Stoop on Thursday 17 September.
It is your chance to join Mark Chapman and a number of World Cup legends including former New Zealand fly-half Andrew Mehrtens, ex-Scotland captain Gavin Hastings, Wales scrum-half Rob Jones and former Ireland winger Denis Hickie amongst his guests.
Tickets are available on the 5 live website.
Sam Burgess has been included in England's 31-man squad for the World Cup, which starts next month.