According to Bloomberg, Welch joined the FCA this month and will report to enforcement and market oversight director Mark Steward.
He joins the regulator from Standard Chartered where he ran its internal investigations unit.
Before that, Welch spent 30 years with the FBI, during which he was deputy assistant director of the cyber division before running its international operations division.
Speaking to Financial Reporter, the FCA confirmed the appointment but had no official statement at time of writing.
Bank of England Deputy Governor Andrew Bailey began his role as the new CEO of the FCA on the 1st July.
He succeeded Tracey McDermott, who acted as interim CEO since Martin Wheatley stepped down from the post in September 2015.