Spencer played the U.S. President's chief of staff Leo McGarry in the Emmy Award-winning show.
The West Wing creator Aaron Sorkin adds in a statement, "John was an uncommonly good man, an exceptional role model and a brilliant actor. We feel privileged to have known him and worked with him. He'll be missed and remembered every day by his many, many friends."
Spencer was nominated as Best Supporting Actor at the Emmy awards each year from 1999 to 2004. He won the award in 2002.
Writers and producers on the show are expected to meet this week to discuss what will happen to Spencer's character. He has already appeared in seven of the 14 episodes of season seven. Filming is due to resume after Christmas.
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