Mr Sappio will be replaced by Houston-based Waldemar Poulsen, who becomes president and CEO. Before Rickmers, Mr Poulsen was Safmarine's Houston-based US country manager.
Group CEO Ulrich Ulrichs thanked Mr Sappio for his role in transforming and improving the company's operations in the Americas.
"Bob's leadership over the last two years has helped to better position our company for the future in the Americas. We are happy he will remain connected to the company in a board role."
Of his successor, Mr Ulrichs said: "We are looking forward to Val Poulsen joining our team. He brings a wealth of experience from Maersk Line and Safmarine to his new role."
In March, the previous Rickmers CEO, Ron Widdows, also former CEO of Neptune Orient Lines and its container unit APL, appointed Mr Ulrichs managing director of the group only to step down himself as chief executive to be replaced by Mr Ulrichs.