England international star Phillips had his medical with City on Friday and the Premier League champions have now announced the signing of the 26-year-old on a six-year deal.
City are paying £42m for the midfielder - rising to £45m with add-ons - but Leeds believe the deal will be worth closer to £50m to them for a player who joined Leeds when he was just 14 years old.
Phillips will wear the no 4 shirt for Pep Guardiola's side.
The midfielder who has become affectionately known as the Yorkshire Pirlo progressed through the club's Academy and made his Whites debut in the Championship clash at Wolves of April 2015.
Phillips eventually became a key cog in the Whites midfield, progressing at a rate of knots under former head coach Marcelo Bielsa and integral in helping fire the Whites to promotion as Championship champions in the summer of 2020.
The Yorkshireman is also now a key member of Gareth Southgate's England side having rapidly amassed 23 caps for the Three Lions.
Phillips leaves Leeds having made 234 appearances for the club, 49 of which have come in the Premier League.
Leeds are looking to sign a new first-team defensive central midfielder to replace the outgoing Phillips.
RB Leipzig's Tyler Adams and RB Salzburg's Mohamed Camara are two of the options that United are keen on.
In the meantime, the Whites are adding a highly rated young centre midfield prospect to their ranks in the shape of 18-year-old Darko Gyabi from Manchester City for £5m.
Gyabi also had his medical with Leeds on Friday and the announcement of the young midfielder's signature is also expected on Monday.