The person was hit by a train between Finsbury Park and Alexandra Palace in London.
They sadly died as a result of the incident.
The incident has resulted in all lines being blocked.
London North Eastern Railway (LNER) said there is no "firm estimate available" as to when the lines will reopen.
Disruption is expected until approximately 4pm.
LNER issued this update at about 12pm: "It is with great sadness to update you, that there has been a fatality between KingsCross and Stevenage.
"I ask you to bear with us whilst we make alternate arrangements for our passengers to travel. I will update as we receive this. Thank you for your patience."
A spokesperson later added: "Due to a person being hit by a train, the following trains will be amended as follows
"12:03 KingsCross to Leeds is now cancelled 12:06
"KingsCross to Lincoln is now cancelled
"12:33 KingsCross to Leeds due is now cancelled.
"Due to a person being hit by a train earlier the 13:36 Harrogate to KingsCross will be terminated at Leeds."