There are also honours for those who campaigned on behalf of wrongfully convicted subpostmasters, after the Horizon IT Post Office scandal.
Sir Stephen, 67, known for BBC comedy Blackadder and hosting quiz show QI, was recognised for services to mental health awareness, the environment and to charity.
He said he felt 'startled and enchanted' after receiving the letter informing him of the knighthood and that it was 'wonderful' to see the charities get recognition.
Sir Gareth, 54, is knighted for services to association football, after leading the Three Lions to the finals of Euro 2020 and 2024, and the semi-final of the 2018 World Cup.
He resigned after England's 2-1 final defeat to Spain in July, having fallen just short of glory in every tournament during his eight-year stint in charge.
Meanwhile, Sir Sadiq, 54, was honoured for political and public service, having been the capital's mayor since 2016.
More than 1,200 people from across the UK received honours in the latest list.
Creator of The Tracy Beaker series Jacqueline Wilson has been made a Dame Grand Cross (GBE) for services to literature, while actress Carey Mulligan and television presenter Alan Titchmarsh become Commanders of the Order of the British Empire (CBE).
Titchmarsh, 75, said telling his wife and daughters about the honour was a 'teary moment.' The top gong goes to Nobel Prize-winning novelist Sir Kazuo Ishiguro, who was made a Companion of Honour for services to literature.
Actor Eddie Marsan has been made an Officer of the Order of the British Empire (OBE) and Myleene Klass becomes a Member of the Order of the British Empire (MBE).
A number of athletes have been recognised after Team GB won 65 m...