Mr Garnier has moved to the post of shadow attorney general, a position that had been held by Dominic Grieve, in addition to his main role as shadow justice secretary.
"Mr Woodward leaves the position of shadow secretary of state with devolution firmly established and he helped play a role in achieving that outcome, " he said.
Shadow home secretary Yvette Cooper said the government had "put chief constables in an impossible position with a 20% front-loaded cut to their budgets".