Premier Kathy Dunderdale says the closure is in line with her promise to run a more efficient government.
The office cost about $360,000 annually.
The position of the province's representative in Ottawa has been vacant for two years.
It was opened in 2004 under former premier Danny Williams, just before relations between the federal and provincial governments began to sour.
Williams said the position gave the province greater access to the federal government, but critics questioned that as his government feuded with Ottawa.