The two will face off Sept. 27 at the MGM Grand Garden Arena in Las Vegas.
Cormier wasn't asked to replace Gustafsson until Wednesday morning, meaning the gamesmanship has gone into top gear quickly.
Jones' young daughter has even got into the act, via an Instagram video.
"DC. My dad's going to beat you up. Guaranteed," said the six-year-old.
"I think it's cute," Cormier told The Canadian Press in an interview Thursday. "Kudos to Jon Jones. Let's sell this fight, let's make people want to watch this fight."
Don't mistakes Cormier's comments for friendship with Jones, however.
The two have not got on since Cormier thought Jones disrespected him in 2010 when they met at UFC 121 in Anaheim where Cain Velasquez, Cormier's training partner, defeated heavyweight champion Brock Lesnar.
"It never stops," Cormier said. "Every time we're around each other, there's something .. It could be a little dig here or a little dig there but there's always something."
In the wake of their fight announcement, Jones sent Cormier a "I hope you're ready to come to daddy" message on social media. Cormier tweeted his response to his followers, saying "I am. I'm going to (mess) you up" with an F-bomb thrown in for good measure.
Cormier also was quick to talk up his "Break Bones" T-shirts.
Tweeted Jones: "This is the fight I wanted in the first place. Nothing like fresh meat #Champion2014"
Cormier, ranked No. 2 among 205-pound contenders, stepped up when offered the fight by UFC co-owner Lorenzo Fertitta, who sent him a 6:30 a.m. text Wednesday. Cormier, who had put off knee surgery to clear up a lateral medial ligament issue, said yes after consulting his coaches.
Cormier (15-0) injured his knee in the leadup to his third-round submission of Dan Henderson in May at UFC 173. It was his second win as a light-heavyweight since moving down from heavyweight.
Cormier called out Jones in his post-fight interview in the cage.
"Jon Jones, you can't run away from me for ever, I'm the kid at the wrestling tournament that is always in your bracket. No matter where you go boy, I'm coming, You better hurry because I getting better."
"If I decide to take Jon Jones down 100 times, I'll take him down 100 times. This is my Octagon, I'm the man," he added.
Now he has a little more than nine weeks to prepare for the title fight.
"Hectic schedule but I'm a very very happy man," said Cormier, while admitting he has work to do to get into fight shape.
The withdrawal of Gustafsson is just the latest bump for UFC 178. The card was originally announced for Toronto but was shifted to Las Vegas in what UFC president Dana White called a business decision.
Jones, who made seven successful title defences since winning the championship belt from Mauricio (Shogun) Rua at UFC 128 in March 2011, won a narrow five-round decision over Gustafsson when they met last September in an epic encounter in Toronto.
Jones (20-1) went on to win a convincing decision over Brazil's Glover Teixeira at UFC 172 in April while Cormier clamoured to meet the champion.
"I've wanted to fight Jon for a long time. I've wanted to be a champion for a long time," Cormier said.
The matchup pits the six-foot-four champion against the five-foot-11 challenger. At 84 inches, Jones has the longest reach in the UFC and will hold a significant advantage over Cormier (71 inches) in that regard.
"I don't care if a guy has long arms," said Cormier. "You've just got to move your head. You've got to be going forward. You can't stand on the outside. Reach becomes important whenever you stay on the outside and you allow a person to use it.
"Him being tall? OK. Josh Barnett was tall. Bigfoot Silva was tall. Soa Palelei's tall. I've fought a ton of tall guys. When I go to the weigh-ins and I look at you in the face and I see your chin right there and if I can reach you with my hands, that's enough for me."
Cormier beat all of those fighters.
The 35-year-old is a two-time Olympian whose wrestling resume includes a fourth at the Olympics and third, fifth and ninth at world competitions. He took up MMA in 2009, making his pro debut in Strikeforce in September that year.
He combines elite grappling with heavy hands, with wins over Roy (Big Country) Nelson and former heavyweight champions Frank Mir and Barnett.
The 27-year-old Jones, a former junior college wrestling champion, and Cormier have similar grappling stats.
Jones averages 2.37 takedowns per 15 minutes compared to 2.17 for Cormier, according to FightMetric. Jones' takedown accuracy is 50 per cent, Cormier 48 per cent. Cormier has never been taken down, while Jones has successfully defended 96 per cent of takedowns.
Their striking stats are also a wash. Jones lands 4.33 significant strikes a minute, Cormier 4.08. Jones' striking accuracy is 54 per cent, compared to 50 per cent for Cormier.
The challenger absorbs fewer significant strikes (1.30) per minute than Jones (1.92) and is successful in his striking defence 70 per cent of the time, compared to 66 per cent for Jones.
Jones has already disposed of elite wrestlers in beating Chael Sonnen and Rashad Evans.
But Cormier believes he matches up well against Jones. And he is clearly watching Jones' every move, including the champ posting a photo of his training partners with the message "These guys will lead me to victory September 27."
Said Cormier: "I've got some guys too. And I've got a big old guy (heavyweight champion Velasquez) that's going to ensure that I'm successful Sept. 27. If you need a training partner, you don't get one better than Cain Velasquez. And then I've got a tall kid (in) Luke Rockhold that's just as athletic as Jon Jones that's going to ensure that I'm ready come Sept. 27.
"So he's got a team and I've got two guys ... Those guys I trust with my life. I'll be ready come fight night."