The 23-year-old, a France Under-21 international, has joined City on a deal until 2023.
Laporte will provide competition for John Stones, Vincent Kompany, Nicolas Otamendi and Eliaquim Mangala in the centre of Guardiola’s defence.
City have also signed English midfielder Jack Harrison from New York City on a three-and-a-half-year deal before sending him out on loan to Championship side Middlesbrough for the rest of the season.
Leicester forward Ahmed Musa has re-joined CSKA Moscow on loan for the rest of the season.
Another player heading out on loan from a Premier League side is Josh Tymon, the 18-year-old Stoke left-back has joined MK Dons until the end of the campaign.
Press Association Sport understands a deal has been agreed in principle between the clubs, subject to Dortmund bringing in their own forward.
The German club have been linked with Gunners striker Olivier Giroud and Chelsea frontman Michy Batshuayi as possible replacements for the Gabon international. The Telegraph says Chelsea are set to bring in Frenchman Giroud, with Batshuayi to join Dortmund on loan.
One player Arsenal will not be signing before Wednesday’s 11pm deadline is Monaco midfielder Thomas Lemar.
The Ligue 1 champions’ vice-president Vadim Vasilyev has reiterated that the France international – also a reported target for Liverpool – is not for sale this month.
“He will stay at Monaco until the end of the season 100 per cent,” Vasilyev told French radio station RMC. “If Liverpool or Arsenal come with a big offer before the end of the market? This is not relevant.”
Southampton’s attempts to sign forward Quincy Promes are being met by resistance from Spartak Moscow, Press Association Sport understands.
Celtic will have to stump up more cash if they want to sign Motherwell goalkeeper Trevor Carson as a replacement for the injured Craig Gordon.
Leicester winger Riyad Mahrez has emerged as a potential target for Manchester City.
Press Association Sport understands City are interested in the Algeria international and have not ruled out making a bid.
Leicester have not received any offers for the 26-year-old this month but their stance has not changed since last summer, when they rejected interest from Roma.
The club do not feel they need to sell and it would take a fee in excess of the £75million Liverpool recently paid for Virgil van Dijk – a defender – to even consider it.