Nicol, coach of the New England Revolution, said: "The stadiums will be full wherever he plays.
"David Beckham is a name and people who would not normally go to games will want to go see him and see what he's all about.
"When it was announced he was coming it was on TV here every day for weeks. Everybody was talking about it, even people who don't know the shape of a football, and although it's settled down a little bit now, I know the interest building up to his arrival will be phenomenal."
MLS communications coordinator Benjamin Ramirez Spencer said: "We started getting calls from CNN, ABC, all the major channels, newspapers and radio stations who really don't cover the game normally. The level of media interest has been really good for us."
Nicol said Beckham will be playing Championship-standard football, adding: "It will be hard for him because of the perception of the standard he will be playing at but if Steve McClaren is prepared to pick Championship players then he could keep his place.
"It is going to be a culture shock coming from Real Madrid where, let's face it, he is playing with some of the best players in the world. He will have to adjust because he will be playing with, and against, a quality of player he is not used to.
"It'll be tough for him at the start and frustrating, but as long as he stays calm and understanding he will do it."