Hawke joined the escorted touring and river cruise specialist from MSC Cruises in April 2016.
He will be leaving at the end of the summer and starting a new, undisclosed, role in the autumn.
Globus said recruitment was "already underway for a successor" to lead the UK business with the aim of "ensuring a seamless transition".
His departure follows that of sales and marketing director Janet Parton to Celestyal Cruises last week, which Globus claimed was "unconnected" to Hawke leaving.
Hawke said: "The last seven years have flown by, and I cannot thank the team enough for their commitment, professionalism, and dedication.
"I’m incredibly proud of everything we’ve achieved both externally with our trade partners and customers and internally with the service we offer and the culture we’ve created. Making the decision to leave has been extremely difficult.”
