Arsenal beat Manchester City 4-1 on penalties to claim the Community Shield after a 1-1 draw at Wembley Stadium on Sunday.
Chelsea have completed the signing of Spanish goalkeeper Robert Sanchez from Brighton & Hove Albion for £25 million.
Manchester City have completed the signing of Croatia defender Josko Gvardiol on a five-year deal from RB Leipzig for £77 million.
Manchester United have completed the £72m signing of Denmark striker Rasmus Hojlund from Atalanta.
Chelsea defender Levi Colwill has signed a new six-year contract with the Blues, with an option for a further year.
Chelsea have completed the signing of teenage midfielder Lesley Ugochukwu from Rennes on a seven-year contract.
Brazil midfielder Fabinho has left Liverpool after signing a three-year deal with Saudi Arabian side Al-Ittihad.
Manchester United have agreed a 10-year partnership extension with Adidas in a deal worth a minimum of £900 million.
Allan Saint-Maximin has become the latest player to join the Saudi Pro League after leaving Newcastle United for Al Ahli.
Manchester United have reportedly agreed on a deal worth £72 million to sign Atalanta striker Rasmus Hojlund.