The 29-year-old, who had less than six months on his contract at the Emirates, arrived at Old Trafford from Arsenal in the January transfer window. As a part of the deal, the Red Devils allowed Henrikh Mkhitaryan move in the opposite direction.
Sanchez came close to joining Manchester City on the deadline day of the last summer transfer window. The deal did not take shape after Arsenal failed to bring AS Monaco's Thomas Lemar to the north London club, reported the Guardian.
Pep Guardiola's side were still believed to be the front runners for the former Barcelona forward's signature in January. However, United were successful in beating City to land Sanchez and the player claims he has now joined the "biggest club" in England.
"I think that Manchester United, since I was young - and I'm not just saying this because I'm here, I'm an honest guy and I never lie - I think it's the biggest club in England. That's what I think," Sanchez told Sky Sports.
"There are lots of big clubs, and having played for Arsenal, they are also one of them. It's a huge club and I was there.
"But coming here, looking at the badge, I think United have to win everything because it's such a big club. The club crest says it all."
"I came here to win [things]. I left Arsenal because I wanted to develop and learn as a player, and get to experience a new club. Manchester United are a huge club on the global stage. I came here to win everything. Otherwise I wouldn't have come here."
Sanchez joined Arsenal from Barcelona in 2014. In his three-and-a-half year spell with the Gunners, he won the FA Cup twice and Community Shield on one occasion.
Sanchez has featured on three occasions in a United shirt. The South American saw his new side suffer a 2-0 defeat at the hands of Tottenham Hotspur in his league debut for the Red Devils. The forward netted his first goal in Jose Mourinho's side's 2-0 victory over Huddersfield Town at Old Trafford on 3 February.