Taylor, who joined the company in June 1994 and is currently customer experience director, will take up her new role on 1 July.
Hawke, whose departure to become the new EMEA chief at Celebrity Cruises was announced last week, will stay on during a handover period through to the end of July.
Taylor will report into Scott Nisbet, chief executive of the Globus Family of Brands.
Nisbet said: “This appointment ensures continuity, stability and inspiring leadership for the team and Lesley will work across all departments to ensure that we continue to focus fully on our customers, our valuable travel agency partners, and our other business partners.
“I have absolute confidence in Lesley’s ability to lead the team through the coming years and continue to grow our touring and river cruise business.”
Taylor said: “I am absolutely delighted to be taking on this exciting and important role and carrying on the good work that we have been doing over recent years.
“I see a big opportunity for our brands in the UK market and have some exciting ideas to deliver even better support for our agent partners, build on our amazing team culture and work with my colleagues globally to ensure we are delivering the best possible holiday experiences for our customers.”