Morrissey has been chief executive of the firm for 15 years, and will stay on as a non-executive chair of Newton's board. She will be replaced by Hanneke Smits, the current chief investment officer at Adams Street Partners.
The appointment raised questions in some parts of the City about the appropriateness of moving from chief exec to chair - something which is cautioned against for listed companies under the Financial Reporting Council's corporate governance code.
As an investment manager and the UK subsidiary of global investment firm BNY Mellon, Newton is not bound by those rules. However, Oliver Parry, head of corporate governance at the Institute of Directors, said: "It is very unusual, but we're talking about a US bank, therefore they are not actually breaking the rules.
"However, it is really important she demonstrates her independence as a non-executive director, especially as she has been chief executive for 15 years. There is a difference between being a chief executive where you're involved day-to-day and being a chair. She has to demonstrate she can exercise that independence."
Peter Swabey, policy and research director at the Institute of Chartered Secretaries and Administrators, added: "There can be circumstances in which this would be appropriate, but it is generally regarded as poor practice and investors would expect a plc to explain the rationale behind the move in some detail. The bar for a convincing explanation would be high."
Morrissey said: "The time is now right for me to move on to the next phase of my career and for a new chief executive at Newton to drive its ongoing growth."
Mitchell Harris, chief executive of BNY Mellon added: "We are extremely thankful to Helena for her many contributions during her tenure as chief executive and I am pleased that she will continue to serve Newton as non-executive chair."
On the appointment of Smits, he added: "She has deep investment knowledge, an impressive track record of developing senior leaders and investment professionals, and proven expertise growing a global firm across developed and emerging markets."
Morrissey, who founded the 30 Per Cent Club to advance the number of women in financial services, will stay on in her role as chair of the shareholders' group the Investment Association.