Bush will join as director of comms and public policy, while Tim Vine, a press officer at the Department for Culture, Media and Sport (DCMS), is joining as head of PR.
Bush replaces Phil French, who is leaving to become CEO of Supporters Direct.
Bush will oversee a comms team of three, to include Vine and incumbent head of press Dan Johnson.
Vine is charged with improving media coverage of clubs' CSR initiatives, such as efforts to boost educational standards in impoverished areas.
Bush and Vine are expected to start next month.
French worked alongside Bush at the DCMS - but left during his induction period to rejoin the Premier League (PRWeek, 28 February 2003).