The company, founded by billionaire Newcastle United boss Mike Ashley, has seen its shares rise 86% since the start of the year.
The FTSE 100 is updated every three months, reflecting changes in the market value of companies.
The reshuffle takes effect from 23 September.
Greek coke bottler Coca Cola Hellenic is also set to join the top flight of London-listed companies after it switched its primary listing from Athens to London earlier this year.
But outsourcing firm Serco has been dropped after its shares fell 8.5% since the end of June.
It is facing an investigation into its practices, and the potential suspension of future government contracts, saw its share price plunge earlier in the summer, before recovering slightly.
Sports Direct, said in a trading update on Wednesday that sales had risen by 18.2% in the 13 weeks to the end of July, compared to the same period last year.

German Kerber, 29, claimed Grand Slam titles at Melbourne and the US Open last year, but lost 6-2 6-3.
American Vandeweghe, 25, faces a last-eight meeting with Spain's French Open champion Garbine Muguruza, who beat Romanian Sorana Cirstea 6-2 6-3.
Venus Williams also progressed, beating Germany's Mona Barthel.
The 36-year-old seven-time Grand Slam champion - the oldest player in the women's singles - won 6-3 7-5 and will take on  Anastasia Pavlyuchenkova, who beat fellow Russian Svetlana Kuznetsova 6-3 6-3.
Vandeweghe's victory was her first against a world number one and takes her to a Grand Slam quarter-final for the second time in her career, after reaching the last eight at Wimbledon in 2015.
It meant the top seed from the women's and men's draws both left the competition on day seven, after Andy Murray's shock defeat by Germany's world number 50 Mischa Zverev.
Vandeweghe had Kerber on the defensive for much of their 68-minute contest, closing out the first set with ease after breaking in the sixth game.
And even though Kerber was able to break immediately in the second set, Vandeweghe won four successive games from 3-2 down for the biggest win of her career.
"It was really special," she said. "Beating the world number one on any stage and any place is great. I'll take this one.
"I wasn't feeling confident - I guess I faked it. I was nervous, but I had a game plan to execute and I knew that as along as I kept picking my spots, I had a chance."
It is 19 years since Venus Williams reached her first Australian Open quarter-final, and 14 years since her one and only final, when she lost to her sister Serena.
In recent years she has had to cope with the autoimmune disorder Sjogren's syndrome - but has managed to reach at least the last 16 at six of the last seven Grand Slams.
Barthel, ranked 118th in the world, had played Williams twice before but missed four months of tennis last year because of chronic fatigue illness.
"I know what it's like to be down on your luck, but she knows how to play tennis and she's experienced," Williams said.
"We'd played a couple of tough matches before so today I expected to have some competition."
Williams, who took one hour and 36 minutes to beat Barthel, has yet to drop a set at this year's Open.
"I've been blessed enough to do something that I love and I think this was my calling because I grew so tall that I can cover the court and hit it hard," she added.
Retailer Sports Direct will enter the FTSE 100 as part of the latest reshuffle of the 100 biggest companies on the London Stock Exchange.
[NEXT_CONCEPT]
Top seed and defending champion Angelique Kerber suffered a fourth-round exit from the Australian Open to world number 35 Coco Vandeweghe.