Fractional Jet Captain reported a NMAC while on final approach and took evasive action per ATC instructions.

Narrative

We had been cleared for the RNAV Rwy X approach at ZZZ; we were on final approach course and had just captured the RNAV glide path; we had flaps 10 set as we were just beginning the approach; airspeed was about 175 kts. Approach called and pointed out traffic to our right and below us which we saw on TCAS but did not see visually. The controller then said 'I hate to do this to you but cancel your approach clearance and fly heading 360'. As we started the turn; the controller said 'Climb!! Climb immediately!! Once we got separation from the traffic; he had us turn to the south and told us that with the traffic there crossing the final approach course the only way he could get us to Runway X would be on a visual approach if we could accept that; which we could as we had the airport in sight by this time; he vectored us back to final and cleared us for a visual approach and we landed uneventfully. As I could see the traffic on TCAS; I saw the traffic with as little as 200 ft. of vertical separation and right underneath us and at no time did we get either a TA or an RA; nor did the target's color change from light blue on the TCAS. As we proceeded with the visual approach; we did get a TA from another airplane in the same area. We also never visually see either airplane.Identification: An excited air traffic controller called us.Cause: NORDO traffic crossing final approach course from another nearby airport.Response: Followed ATC's instructions and took evasive actions"