The Tigers pulled off something of a coup by signing the 21-year-old from the Gunners on a three-year deal.
To make a further addition in McCormack, however, it is understood Hull will have to off-load at least one more player following Daniel Cousin's switch to Greek side Larissa this week.
Simpson will go straight into the squad to face Watford today and Hull manager Pearson said: "He has been at Arsenal for a number of years and been out on loan at several clubs. But now it is a chance to prove himself.
"In Robert Koren and John Bostock, it gives us the possibility of more goals. Most people would agree it's an area we need to look at."
Koren, who signed a two-year deal last week, is in line for his full debut.