The England international, 26, is undergoing a medical with the Premier League champions on Friday and the transfer is expected to be announced imminently.
Phillips has emerged as one of the top-flight's most highly-rated players and a regular starter in the Three Lions' midfield in recent years.
With two years remaining on his contract, and given his sheer importance to Jesse Marsch's side, many expected Leeds to value Phillips at more than £42m.
The Whites are thought to have rejected a £50m bid from West Ham in Janaury.
And ex-Leeds and City defender Danny Mills insists Leeds should have got more cash for their star player.
He said: "I think it's a little bit cheap for Kalvin Phillips. I'm a little bit surprised by that.
"He's got two years left on his deal, there was no desperation to sell. Kalvin wasn't desperate to go, either.
"He wasn't banging the doors down saying, 'Let me go, let me go!'
"It's a fantastic move for them. I don't think he goes straight into their starting XI but he will challenge.
"He's an experienced England internatonal now, he's 26-years old, he's a very good player.
"When they were talking about £55m-£60m from West Ham in January, I thought they would have to go to £70m.
"To go to £42m? It's a good move for Phillips, Leeds were going to have to sell him at some point, I just think that's a bit cheap."
However, ex-Crystal Palace owner Simon Jordan does not agree with Mills' assessment of Phillips as a player.
Jordan said: "I don't look at this and say it's particularly bad business.
"I'm not in the camp that Phillips is a wonderful player. I think at £42m - he's alright, he's OK.
"I think he's a symptom of a certain type of player. He's OK."