The teens are accused of breaking into a home in Cairns and threatening a couple with a knife early on Friday morning, before taking a woman into a separate room.
Police allege they then sexually assaulted the woman before fleeing the home.
It is understood the alleged offenders were not known to the victims.
Two of the teenagers were arrested about an hour later and hit with a string of charges.
The third was arrested shortly before 6pm on Friday.
Dramatic vision of the arrest shows police in a lengthy sprint after a 15-year-old, who ran across multiple lanes of traffic on a busy road.
Police then tackle him on the median strip and handcuff him.
Detective Inspector Kev Goan labelled the incident "horrific".
"For a young couple to be in bed, to have their home invaded by three intruders and for the male to be held at knifepoint while his partner is subject to sexual assaults while her assailants are also armed," he told News Corp.
"The impacts of the offending will have a significant impact on two victims and our deepest sympathies go out to those two victims."
A 15-year-old boy and a 16-year-old boy have each been hit with five charges of rape, along with armed robbery, deprivation of liberty and break-and-enter charges.
They are expected to face the Cairns Children's Court on Saturday.
The third teen is yet to be charged.
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