Chile international Sanchez made the switch in a straight swap deal with the Gunners, as Henrikh Mkhitaryan moved to the Emirates Stadium.
Wales boss Giggs wrote in a column for Sky Sports News that United boss Jose Mourinho has been given an extra selection headache due to the arrival of Sanchez.
"Manchester United signing Alexis Sanchez is similar to Robin van Persie in the sense that they're getting a ready-made superstar and you're seeing the contribution already with Anthony Martial upping his performances," he wrote.
"That can happen when top players come in, those around them lift their levels, and there will be some difficult selection decisions for Jose Mourinho.
"However, Sanchez can also play on the right, as he did at Barcelona, so if Martial is flying then he may have to play in a different position, but those sort of decisions are positive for a manager to have to make."
Sanchez will be available for United's Champions League last-16 tie against Sevilla after featuring in the Europa League for Arsenal prior to his Old Trafford switch.