Two Swiss banks have become the latest in a long line to reach an agreement with US authorities under the Department of Justice’s Swiss Bank Program.

Cornèr Banca SA (Cornèr) will pay a fine of $5.068 million to avoid prosecution after it aided US taxpayers in evading their tax obligations. It is based in Lugano with offices in Chiasso, Geneva, Locarno and Zurich, Switzerland.  It also has two wholly owned affiliates Cornèr Banque (Luxembourg) SA, based in Luxembourg, and Cornèr Bank (Overseas) Ltd., based in the Bahamas.

Basel-based Bank Coop was fined $3.223 million for...