Moyes has been desperate to experience the pinnacle of European club football, so much so it was assumed he would leave Goodison Park in the summer before United made their move.
Finally, 15 years after stepping into management with Preston, the Scot gets his chance.
"I am really looking forward to the Champions League," said Moyes.
"I have been there with Everton but we didn't quite make the group stages.
"This is something different. I'm now managing a club which is used to getting close to the final stages and I will try and do that again."
Moyes has already revealed predecessor Sir Alex Ferguson told him a group containing Shakhtar Donetsk and Real Sociedad, in addition to Tuesday's opponents, is one of the toughest he can imagine.
And whilst Moyes pointed out his opposite number, former Liverpool defender Sami Hyypia, is also a rookie in the competition, it is an indication of the leap he has made that the man he will be most keen to stop on Tuesday, last season's Bundesliga top scorer Stefan Kiessling, was someone he looked at but knew he could never afford whilst he remained at Everton.
"He has a great goalscoring record," said Moyes.
"He has a smell for getting on the end of chances and is someone we will need to watch very closely. I didn't try to sign him though. I never had that much money."
Moyes' opposite number Sami Hyypia returns to Old Trafford on Tuesday night hoping his experience is more like his best day against United rather than his worst.
A veteran of a decade's service at Liverpool, Hyypia has plenty of experience on the ground which will mark his debut as a Champions League manager.
Indeed, his final start as a Liverpool player came there, when Fernando Torres inspired a remarkable 4-1 win.
Yet just as sharp in the Finn's memory is a visit six years earlier, in 2003, which did not end quite so well.
"I was sent off after four minutes and watched the rest of the game in the dressing room," he said.
"It was the only red card and we lost 4-0.
"You remember those kinds of things but the first one that comes to my mind is playing my last game here, when we managed to win 4-1.
"I only knew I was playing two minutes before kick-off and it was my last 90 minutes for Liverpool."
Hyypia hopes to exploit some uncertainty in the Old Trafford camp even if, ultimately, he expects Moyes to be a success in his new job.
"It is not the first year they have started slowly," said Hyypia.
"They are at home, they have bigger experience in the Champions League and the pressure is on them.
"We are more relaxed but we must make sure we do not not show them too much respect.
"David Moyes is an experienced manager though. Everyone should give him more time to get things running. I just hope it doesn't happen tomorrow."