Long has moved to The Hawthorns for an undisclosed fee believed to be an initial £4.5 million and rising to what would be a club record £6.5m.
The 24-year-old Republic of Ireland international - in action for his country tonight against visiting Croatia - is Hodgson's sixth signing of the summer.
Long has signed a three-year contract with an option for a further 12 months.
Hodgson said: "Many other clubs have shown an interest in Shane and it is great that we have managed to acquire his services.
"With the signing of Shane, our squad is looking close to being complete."