While there were initial teething problems, Klopp's Liverpool have developed into something special over the past two years.
"It's an wonderful place to play football, it's an unbelievable time to be at the football club".
Liverpool defeated Tottenham to be crowned European champions for a sixth time in July and are now eight points clear atop the Premier League as they look to claim a first English title since 1990.
"The club was asking for a while already if we could talk about an extension and I thought it makes sense before things are getting a bit intense ― not now, I was completely calm ― but maybe in the summer we would have started again", Klopp said at his pre-match press conference.More news: Strictly Come Dancing 2019 results! Who left? Latest celebrity voted off
Klopp's assistants, Peter Krawietz and Pepijn Lijnders, have also agreed deals to continue with the club.
There were fears that Milner could potentially leave the Reds with his previous deal expiring at the end of the season and there were rumours of him potentially making a return to Elland Road and his boyhood clubs Leeds.
Mourinho said."And good news for the Premier League, we want the best players & coaches and he's one of the best".
Georginio Wijnaldum suffered a muscle injury in Saturday's 2-0 win over Watford.More news: Colin Firth and wife split after 22 years of marriage
This season, they are well poised to end their 30-year wait for a top flight league title after going unbeaten in the first 16 games, with an eight-point lead over second-placed Leicester City.
"First of all, it means they are all happy". Salzburg's Takumi Minamino is poised to be his first signing when he arrives in January for just £7.25million and Klopp has also highlighted how important youth is at Anfield.
"For anyone in football who aspires to compete in an environment where every element of the organisation is at its very best - from the support of the supporters to the vision of the owners - there can be no better place than this".
The fresh terms for vice-captain Milner came on the same day the club renewed manager Jurgen Klopp's contract until 2024.More news: Fortnite will get an annual battle pass with exclusive skins
The 33-year-old joined from Manchester City on a free transfer in the summer of 2015.