Challenger 605
Situational Awareness
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
Approaching runway 31L at BFI inside the OM tower advised us of helicopter traffic departing southeast bound and that the helicopter would 'remain southeast' of the final.  Watching diligently for the rotorcraft I asked for flaps 45 and final landing items. Checklist was complete and I Pilot Flying (PF) and the Pilot Monitoring (PM) observed the helicopter on TCAS but did not have visual. Getting closer it was evident the helicopter's [track] was NOT remaining Southeast of the final and instead was veering into the final. I began to verbalize my intentions to the PM that we would be prepared to level; or potentially execute at TCAS climb and go-around as available airspace to conduct an RA maneuver and transition back to a stabilized approach was rapidly diminishing. The traffic continued on its near collision course with us edging even closer to centerline. I had already disengaged the autopilot and noted the helicopter was showing 400 feet below our altitude. The PM called visual with the traffic - and I spotted it as well. I advised I was leveling at the same time the TCAS resolution advisory issued a climb followed by a softening command (I don't remember what it was). Ultimately I climbed only a little bit before hearing clear of conflict. As I had barely climbed more than a dot high I determined I could successfully return to the glidepath and maintain stabilized approach criteria. Glideslope was maintained and landing occurred at the 1500 foot point. The traffic passed 400 feet below our altitude and nearly right below our flight path (i.e. nearly on centerline). This was absurdly dangerous on the part of the rotorcraft pilot and highly nonsensical.
A CL-605 pilot reported an NMAC with a helicopter on approach to BFI.