Zaha was signed from Crystal Palace by United in January, before being loaned back to Selhurst Park for the remainder of the season and helping the Eagles gain promotion via the play-offs.
There has been speculation that he could agree another loan deal with Palace for the new season, although it will be down to United to decide on the best course for his development.
Freedman played a key role in helping Zaha flourish during his time at Palace, and is backing the 20-year-old to go from strength to strength with the Red Devils.
However Freedman, who left Palace in October to take charge of Bolton Wanderers, says it would be wrong to expect an immediate impact.
"It took him eight games to establish himself in the Palace first team and eight to 10 games later he was the best player," said Freedman.
"I have no doubt he will take time to settle in but when he does he will show the talent that he has.
"I know his character and he won't be fazed, David Moyes will see that day-in and day-out.
"Wilfried likes a challenge, hence he's gone to the biggest club in the world."