McPherson joins the bank from Edinburgh Council where she was its chief comms officer.
At Co-op Bank, McPherson will head up the comms team, overseeing internal comms, media relations and public affairs, as well as values and ethics.
The bank suffered embarrassment in 2013 after its former chairman, Paul Flowers, was convicted of drug possession after he was caught on camera attempting to buy crystal meth.
The incident occurred six months after he had resigned from Co-Op, shortly after it emerged that there was a £1.5bn black hole in the bank’s finances. PR professionals last year praised the company for its "refreshing honesty" in dealing with the aftermath of this.
McPherson said: "As the only UK bank with a customer-led ethical policy at the heart of its business, I think there is a real opportunity to develop a distinctive story that resonates with customers... There’s great potential in bringing the bank’s values and ethics approach to the centre of its communications strategy."
McPherson’s previous experience includes a long stint with the insurance and pensions company Aegon UK, where she was comms director.
Niall Booker, chief executive of The Co-operative Bank, said: "Lesley joins the bank at a time when our brand is on the up and I believe she is the right person to continue that momentum and really drive the message of how deeply embedded values and ethics are in our bank."