The 19-year-old was United's only deadline-day signing and will initially link up with Warren Joyce's reserve-team squad before pushing for a chance at senior level.
Skipper of the Swiss Under-17 side crowned world champions in 2009, Veseli hoped to get his chance at City this term after being part of Roberto Mancini's squad for the pre-season tour of the United States.
However, the opportunity never came and as Veseli grew disillusioned, in stepped United, whose manager Sir Alex Ferguson has never been afraid to give youngsters a go.
"These days, Manchester City are chasing titles and major trophies," explained Veseli's agent Adam Bouskouchi said.
"It is difficult for them to have faith in youth because they obviously feel experience is the best way for them to get where they want to go.
"But that attitude didn't help Freddie, who just felt like he wasn't progressing.
"On that pre-season tour, both Roberto Mancini and - director of football - Brian Marwood said how well he had done. But since then, nothing."
In fairness to Mancini, he does not have 12 league titles to fall back on if he gets it wrong.
It cannot be underestimated how much strength that gives to Ferguson, who handed Ben Amos and Paul Pogba their Premier League debuts in Tuesday night's win over Stoke.
"Freddie spoke with several clubs, here and abroad," said Bouskouchi.
"But he wants to be a top player in England and when Sir Alex spoke to him, it made such an impression.
"He is a difficult man to say no to and his track record was enough for Freddie to feel he was making the right choice to join United."
As City are not part of the Premier Reserve League, Veseli is lacking match fitness at present.
However, his aims are clear, both in the short-term and then later in the year, when Switzerland will be amongst the countries competiting at the London Olympics.
"First his challenge is to establish himself at reserve level, then push on for the first team," said Bouskouchi.
"But the Swiss Federation have also been in touch and they are keeping track of him.
"However, they have said Freddie must at least be involved at reserve team level before they could consider him for the Olympics."
