Charles Horton said “I recognise that passengers have been hugely frustrated at the significant disruption caused by the introduction of new timetables.
“It is the right time to hand leadership of GTR to a new pair of hands.
“I am immensely proud of my team and I would like to thank my 7,000 colleagues at GTR for all their hard work over the past four years.”
The new timetable was introduced on 20 May and was intended to last until the end of July, “stabilising” services and eventually reducing last-minute cancellations.
Instead, it resulted in 5% of services on the Southern, Thameslink and Great Northern lines being cancelled and about 18% of them being delayed.
Southern passengers have also endured dozens of days of industrial action over the past two years due to a dispute between the company and the Rail, Maritime and Transport union about having guards on trains.
Martin Abrams, spokesman for the Association of British Commuters, said Mr Horton “presided over one of the worst crises we’ve seen on the privatised railway” and his resignation is “the absolute least that passengers who use Govia Thameslink Railway could expect”.
He added: “Whether Charles Horton is being used as a fall guy for (transport secretary) Chris Grayling, who really is ultimately responsible for the debacle we’ve seen, is another question.”
Mick Cash, general secretary of the RMT union, which has been striking on Southern services over the role of guards, said: “Mr Horton may now have gone but the rotten franchise he was steering remains in place and no change at the top will alter that.
“This whole basket-case operation is a failure on every level.”
GTR runs the Thameslink, Great Northern, Southern and Gatwick Express services.
It is a subsidiary of Govia, a joint venture between Go-Ahead Group and French company Keolis.
Go-Ahead Group said Mr Horton will remain in the post for a short period to oversee the development of a temporary timetable to address the recent problems.
David Brown, group chief executive of Go-Ahead, said: “Under often challenging conditions, he has built a team to deliver the largest railway change programme for decades, on a franchise that is not only the UK’s biggest, but which has also has seen the highest passenger growth.”