Hatswell is leaving her post of four years following her departure from the EDF Energy London Eye at the end of August, which gives her more time to take on the general manager role.
The Royal Opera House's head of commercial programming Moya Maxwell will take the reigns as acting chairman.
Hatswell has spent 10 years at UVL, seven of those on the board. She will become general manager from next month.
The position is the first of its kind at UVL, which is run by board members who are volunteers from its membership base. Hatswell will assist the acting chairman in growing the organisation’s membership base and managing its marketing and events programme.
Hatswell said: "UVL has long been part of my career and I am delighted that I can continue to support all its work in the industry as its first general manager.
"As the organisation has continued to develop over the years, a real need has evolved for additional behind the scenes support for the board and membership. UVL is going from strength to strength and I am pleased to be able to continue on its exciting journey".
Maxwell added: "I hope to continue [Hatswell’s] excellent work as acting chairman and I look forward to continuing to advance UVL as a leading consortium of iconic venues in London."