The striker spent eight years with the Gunners before joining United for a fee of £24m and landing his first Premier League title last season.
The 30-year-old has been in fine form since moving to the Red Devils and, although Moyes admits that he understands Arsenal's frustration, he believes that the Dutchman wanted to leave and was right to choose United.
"Robin was a great player at Arsenal, and he's come to Manchester United and been the same," Moyes told reporters.
"I can understand Arsenal being a bit upset about that. Nobody wants to let their best players leave and Robin was undoubtedly one of Arsenal's best players.
"But his contract was running out, there was a situation where Arsenal had to act and Manchester United wanted him. Robin must have had strong views about wanting to join United at the time and I am sure he'd say he's made the right choice."
Arsenal travel to Manchester to face Moyes's side this afternoon.