He will take up the position on October 31 when current chairman Bill Mustoe steps down at the company's AGM.
Paice, who served as minister of state for Agriculture and Food from 2010 to 2012, has held the position of MP for South East Cambridgeshire since 1987.
Paice said he felt “privileged” to have been offered the role."The dairy sector has gone through difficult times recently but I have long believed there is a good future for British dairy farmers and I look forward to helping to achieve it," he added.
First Milk chairman Bill Mustoe said Paice would bring valuable skills to First Milk.
"As a former minister of state responsible for agriculture and food and shadow minister for Agriculture & Rural Affairs for six years prior to that, he brings considerable knowledge and experience of not only the domestic market, but also the international dynamics of the dairy industry.
"He has been a champion for farmers at Westminster for over 25 years and we now look forward to him being a champion for First Milk farmers."
Meanwhile, Jim Baird, Willie Campbell and Wendy Radley will replace Tom Campbell, Mark James, Hugh Parker and Simon Weaver as farmer directors, subject to member approval.
First Milk is reducing the number of farmer directors on the Board from six to five, which is in line with the streamlining that has been brought to other roles across the business.