The company said it would appoint Ian Marchant as executive chairman while it looked for a new CEO.
"It was felt this was the right time for new leadership to take on the operational and delivery challenges for the next regulatory period (2020-25)," a spokesman for Thames Water said in an emailed statement.
Robertson, who was appointed in September 2016, was previously chief executive at telecoms services companies Truphone and BT Openreach.
He will remain at Thames Water until June 30 to help with the transition, the company said.
Britain's utilities are facing the threat of nationalisation after the leader of Britain's opposition Labour Party Jeremy Corbyn said he would take the country's water, electricity, gas and railway operators into state ownership should it win a general election.
Thames Water, which has not provided many details about how it would respond to nationalisation, in April added a clause to its outstanding bonds ensuring lenders would be paid back immediately in such a situation.
Other water utility companies, including United Utilities and Severn Trent, have warned that renationalisation could have an impact on their profits.
Last week, the head of electricity and gas utility company National Grid said renationalising energy networks would increase costs for consumers and could prompt legal challenges.
(Reporting by Samantha Machado in Bengaluru; Editing by Arun Koyyur, Shinjini Ganguli and Kirsten Donovan)
By Samantha Machado