In a statement, the authority said Mr Jones had confirmed to his fellow authority members on Tuesday night that he had tendered his resignation to Secretary of State for Culture, Media and Sport Jeremy Hunt.
That run of reaching five successive major finals - and his time in charge of Sweden - was halted by failure to qualify for the 2010 World Cup in South Africa and Lagerback tendered his resignation.
It is a quirk of the Church's practice that Cardinal O'Brien had already tendered his resignation, as he approached his 75th birthday, the official retirement age for bishops.
Earlier in the day, Mrs Clinton officially tendered her resignation to President Barack Obama, her former bitter rival in the 2008 race for the Democratic presidential nomination.
"I'm very sorry that without even waiting for an update at this afternoon's gathering of the transport advisers Pip Sheard has tendered her resignation, " Mr Ferguson added.