Alderman Warke, who is the current deputy mayor, has been a councillor for the Faughan ward since 2015.
The Newbuildings politician was co-opted by to fill the vacancy on the council left by Gary Middleton when he became a Foyle MLA.
In the 2019 council elections, Alderman Warke topped the poll in the Faughan ward.
He will take up the role of Mayor at the council’s annual general meeting in June.
Alderman Warke said: “It is an immense honour to have been put forward by my party to serve as Mayor in the incoming year.
“I look forward to serving all of the people of Londonderry and Strabane during my term in office.
“As the recovery from the COVID pandemic continues, now is the time to look ahead and enjoy these hard won freedoms safely as we see restrictions being relaxed.
“We must continue to do all we can as a community to keep ourselves and each other safe and l appeal to everyone to be cautious to help ensure we can keep moving forward in the right direction.
“I want to thank my colleagues for putting their trust in me to hold this position, especially as this is the Northern Ireland Centenary year. I look forward to representing the council area to the best of my ability.”
DUP Foyle MLA Gary Middleton said Alderman Warke will be an “outstanding” Mayor.
“Graham has always had a strong focus on communities and helping those in need.
“I am confident that he will use his term in office to champion our communities and the many great people within them. I wish him all the best for the year ahead.”