Hodgson has ended his 15-month spell in charge at the Hawthorns to become England's new head coach in succession to Fabio Capello with a four-year contract confirmed.
The 64-year-old will remain in charge of the Baggies for the final two Premier League matches of the campaign - away to Bolton on Sunday and home to Arsenal on May 13.
But Peace is already turning his attention to finding a replacement for the former Liverpool boss who has guided Albion into the top 10 this season.
Peace said: "The board will now concentrate on the important task of appointing a new head coach to continue our project as we prepare for a third successive season in the Barclays Premier League.
"We did not want Roy to leave and he will be a tough act to follow. But I want to reassure our supporters that we will do everything possible to identify and appoint the right head coach for this football club."