Detective Inspector Greg Williams said the arrests come as a result of a "wide-ranging and detailed'' police probe.
He said the tragic victim's family were "very relieved'' at the developments.
"As you can imagine this has been an incredibly hard time for them,'' the detective inspector said outside Christchurch South police station.
He said officers had recovered a "significant'' amount of property that was taken from Jade's home on the day of the murder from a number of second-hand dealers, from the 34-year-old male's home, and from an area at McLeans Island outside Christchurch.
Mr Williams said: "The investigation still continues for us even though these people have been charged.
"What we're doing now is focusing in on some specific times, principally activities at the home between, we think, about 10am and 10.35am when the burglary probably occurred, and I think probably the murder occurred.
"And again, at about 1.20pm when we believe that the 34-year-old male went back to the address at which time the fire was lit and further items taken.
"We're obviously still interested in the movements of that green (Mitsubishi) Diamante station wagon which belongs to the 34-year-old and clearly in the movements of the two men. That is still the focus for us.''
He added: "The area canvasses are nearly completed now. The scene team will be at Barrington Street for another couple of days yet.''
The detective inspector confirmed that the two men were known to the Bayliss family, adding: "One of the men was briefly going out with the mother of the deceased.''
Police earlier confirmed Jade was assaulted some time before the blaze which was reported to emergency services by the public shortly before 1.30pm on Thursday.
A member of the public found Jade's wallet on the rooftop carpark at the mall soon after 12.30pm on Thursday and handed it to the mall's management.
Jade's parents, Gary and Tina Bayliss, have asked for privacy while they grieve the loss of their "beautiful daughter.''
Mark Wilson, principal of Cashmere High School where Jade attended, said the school community was shocked and saddened by her death.
He described her as an outstanding student with an exemplary school record whose motivation and hard work put her near the top of her class.
Mr Wilson said: "She had a quiet and shy nature, yet was also a very friendly and positive person, who was held in the highest regard by all her teachers.
"Our school students and staff will struggle to realise and accept that we have lost this delightful young person.''
