England midfielder Beckham, who will join Milan on loan from LA Galaxy for the second consecutive year in January, was granted his wish after saying this week he wanted an Old Trafford return after a seven-year absence.
"I think it'll be a beautiful, extraordinary match. These are great matches to play, to experience in every sense," Milan coach Leonardo told a news conference on Friday.
"In this case there is Beckham's situation, which is a very beautiful thing for him and for us. Every clash has its ingredients that can contribute to making it more beautiful.
"These meetings give extra colour to the great clashes, with (Karim) Benzema going back to (Olympique) Lyon, (Zlatan) Ibrahimovic meeting Inter again and Kaka meeting Milan again (in the group stage), (Jose) Mourinho against Chelsea again."
Beckham left United for Real Madrid in 2003 having won six Premier League titles and the 1999 European Cup with the club.
Milan fans might take the draw as a good omen as their team knocked out United in the semi-finals on the way to their seventh victory in the competition in 2007.
"I think they're a team of great tradition with the same objectives that we have and we'll play on level terms," Leonardo said. "They're a great team, of course."
The draw also pitched Inter Milan boss Jose Mourinho against his former club Chelsea, whom he led to the 2005 and 2006 Premier League titles.
"It's better to have strong motivation and against Chelsea there will be that," Inter president Massimo Moratti was quoted as telling a local TV network by the club website (www.inter.it).
"There's no use being afraid and I don't think we will be. I think it will be an extra stimulus for Mourinho to return to Stamford Bridge.
"We all drew strong teams. Only Barcelona had a good draw, but you never know in football. Milan will have a beautiful challenge too."
