Board chairman Ross Laidlaw said the changes were caused by the duo picking up other commitments which meant they did not have the time to commit to the Highlanders.
Eagle was appointed to the Highlanders board by the New Zealand Rugby Union after the board was significantly reshaped in 2009.
A Christchurch company director, he was appointed as the chairman of the New Zealand Rugby Union late last year after Jock Hobbs resigned because of ill health.
Laidlaw said because of this commitment and other jobs, Eagle would stand down as the national union's representative on the Highlanders board.
He had yet to formally resign but would do so shortly and a replacement from the NZRU board would be announced in due course, Laidlaw said.
Smith was the Dunedin City Council representative but has tendered her resignation from the Highlanders board.
Smith has been appointed secretary-general of the New Zealand Olympic Committee and has moved to Wellington to take up that position.
Laidlaw said he had been talking to the council about getting a replacement but the council had yet to select a representative.
Smith was appointed to the board in December, 2009.
