They will buy 35 stores, while another 30 which are not part of the deal will close with the loss of 92 jobs.
The buyer is investment vehicle Enact, a small business fund.
It is backed by investors including former Leeds United full-back Mr Mills and Tim Whitworth, founder of the Republic fashion chain.
Before the deal West Cornwall Pasty, which has its head office in Buckinghamshire, operated 20 railway station-based outlets as well as 45 in other locations.