City have reportedly paid £37mn (B1.7bn) for the 20-year-old fleet-footed winger, who has just four caps for Germany and 47 Bundesliga appearances under his belt for Schalke.
Sane has bags of potential and will be battling England international Raheem Sterling for playing time at City.
He will add to the attacking options for City coach Pep Guardiola with Sergio Aguero, Kevin De Bruyne, David Silva, Wilfried Bony, Jesus Navas and Samir Nasri also vying for starting places.
The Premier League is arguably the world’s most high-profile and physically demanding domestic competition, which, unlike some of its continental cousins, does not break for winter.
Sane announced his arrival with a spectacular Champions League goal in March 2015 at Real Madrid in Schalke’s 4-3 away win in the last 16, as they bowed out 5-4 on aggregate, which led to his first Germany call-up at the end of last year.
Many Schalke fans feel Sane’s move has come too soon, something he rejects.
“I have read many of your comments on social media and many are of the opinion that this switch has come too soon,” he wrote on Instagram in an open letter to Schalke fans.
“I wanted to simply use this chance. You never know what is going to happen in the future and when you’ll get an opportunity like this again.
“My family and I had a lot of conversations with Pep Guardiola, who has totally convinced us of what he wants to achieve in England and internationally in the next few years.
“I feel prepared to make this next step, but you can believe me when I say I will never forget Schalke.”
Sane’s sentiments echo the tears shed by Manuel Neuer, another talent nurtured by Schalke’s academy, in announcing he was leaving to join Bayern Munich in 2011.
But as former Germany captain Bastian Schweinsteiger is learning at Manchester United, having been made to train with the reserves by manager Jose Mourinho, a dream move to England can quickly sour.
The 32-year-old Schweinsteiger has struggled to cope with the physicality of playing in England and was blighted by knee injuries last season.
Japan’s Shinji Kagawa signed for United in 2012 while in great form having helped steer Borussia Dortmund to the league and cup double.
He became the first Japanese to win the Premier League, but after Alex Ferguson left Old Trafford in 2013, Kagawa was benched by his successor David Moyes and rejoined Dortmund in 2014.
Another example is ex-Schalke midfielder Lewis Holtby, who joined Tottenham Hotspur as a 23-year-old in 2013 with a handful of Germany caps, but after two unfruitful seasons at White Hart Lane, he signed for Hamburg last year.
Andre Schuerrle struggled to hold down a first-team place at Chelsea, and is now at Borussia Dortmund after a short spell with Wolfsburg.
Mesut Ozil has made a success of his 2013 transfer to Arsenal and is a first-choice of Gunners boss Arsene Wenger.
But his Germany team-mate Lukas Podolski was shipped to Inter Milan, then Istanbul’s Galatasaray in 2015, after falling out of the Frenchman’s favour.
Sane joins fellow Germany squad member Ilkay Gundogan, who signed for City from Dortmund and will also be under pressure to perform after back-to-back injury-ravaged seasons with Borussia.
Former City and Germany midfielder Dietmar Hamann is backing Sane to be a success.
“He’s a very gifted player technically and he’s got a lot of pace,” Hamann told Sky Sports.
“He’s not been prolific for Schalke over the last couple of seasons but I think he is a player who can, and will, score goals.”