The 21-year-old joined the Citizens' academy from Derby County in 2019 and established himself as one of the club's brightest prospects in their Elite Development Squad.
Delap scored 35 goals in 36 appearances for Man City's Under-23s, before netting his first senior goal on his debut for Pep Guardiola's side in an EFL Cup win over Bournemouth in September 2020.
The striker went on to make just five more first-team appearances for Man City and was sent out on loan to Championship trio Stoke City, Preston North End and Hull City, scoring eight goals in 31 league appearances for the latter last season.
With his pathway into Guardiola's first-team plans blocked by the likes of Erling Haaland and Julian Alvarez, Delap has opted to depart the Etihad Stadium permanently and join Ipswich on a five-year deal until June 2029.
Delap to be 'important Ipswich player' for 'many years to come'
Delap becomes Ipswich's fourth signing of the summer transfer window after Omari Hutchinson, Ben Johnson and Jacob Greaves, the latter was unveiled as a new Tractor Boy on Friday after leaving Hull.
"I'm really excited," Liam told TownTV. "I have heard so many good things about the feeling around the club, and how the players and staff work. That's exactly why I'm excited to be here.
"The manager here likes to play exciting football. It's quick and intense and I am looking forward to that. I want to bring goals and assists and I'll work as hard as I can to help the team."
Manager Kieran McKenna added: "We are delighted to bring Liam to the club. We think he is a player with the qualities to help the team this season but also to be an important player for the club for many years to come.
"He is a player with outstanding physical and technical attributes who has a hunger to come here and continue to learn and improve. He has gained good first-team experience from a young age and we feel he has the potential for development here."
Delap sale takes Man City's summer earnings over £50m
Man City will allegedly receive an initial £15m for Delap plus an additional £5m due in potential add-ons, meaning that they have now generated over £50m this summer, predominantly from player sales.
Delap is the third Citizens player to be sold to a Premier League club this summer after Taylor Harwood-Bellis, who has joined Southampton for £20m following a successful loan spell last season, and Tommy Doyle, who similarly has made his move to Wolverhampton Wanderers permanent for £4.3m after a year on loan.
On Friday, Man City pocketed around £8.4m from the sale of left-back Sergio Gomez to Real Sociedad, while they have also received £1m from League One side Stockport County for academy graduate Lewis Fiorini.
Meanwhile, the reigning Premier League champions benefitted from Aston Villa's sale of Douglas Luiz to Juventus earlier this summer, as they have earned a fee between £5.4m and £8.5m due to a sell-on clause inserted into the midfielder's deal when he moved to Villa Park in 2019.