The Argentine international will join the Premiership champions in a British record £28.1m deal from Italian club Lazio.
And the 26-year-old revealed he was swayed by the advice of England manager and former Lazio boss Sven Goran Eriksson.
"I definitely want to sign for the club. It would fill me with pride to wear the shirt of Manchester United," Veron told the Daily Mirror.
"I spoke extensively with Mr Eriksson, with whom I have an excellent rapport.
"He gave me a lot of advice and explained a lot of things. He really pushed me hard to come and play in England.
"But above all, Manchester United are a great team. And the team is always greater than any player."
Veron expects to be in Manchester next week to undergo a medical.
"As far as I'm aware there are no real obstacles to prevent me joining United," he added.
"My representatives will go to Manchester to meet the club's chief executive this week and surely they will come away with an agreement."
Veron was impressed that United had shown their interest before his high-profile case where he was cleared of providing false papers to obtain an EU passport.
That puts United ahead of Milan rivals Inter and AC in the race to sign Veron.
"United have the best chance because first and foremost they came to me before the disciplinary sentence and they made me feel their interest and support," he said.
Earlier, David Beckham said he wanted Veron to become the newest high-profile recruit to the Manchester United squad.
The England captain believes he can form a world-class midfield with the Argentine international.
"I hope Veron will be with us in pre-season training," said Beckham.
"He's a very good player. In fact, I'd go as far as to say he's a brilliant player. He's one of the best in the world."