Ms Rayner resigned after an ethics adviser concluded she breached the ministerial code by failing to pay the correct stamp duty on a property.
The reshuffle aims to relaunch the government as it struggles in polls and to deliver on key promises.
Key ministerial changes include David Lammy becoming Justice Secretary and Deputy Prime Minister, Shabana Mahmood moving to the Home Office, and Yvette Cooper to the Foreign Office.
Other significant appointments see Steve Reed take over as Housing Secretary, Pat McFadden lead a new 'super ministry' for welfare and skills, and Douglas Alexander return as Secretary of State for Scotland.