Simpson was arrested shortly after 11 a.m., Capt. James Dillon said.
The charges against Simpson will include robbery with a deadly weapon, conspiracy to commit robbery and burglary with a firearm, all felonies, Dillon said. More charges could be brought against him, he said.
Simpson was being held at Las Vegas police offices pending the arrival of his lawyer, who was expected later Sunday, Dillon said.
"He was very cooperative, there were no issues," Dillon said.
At least one other person has been arrested and police said Sunday that as many as six people could be arrested in connection with the alleged armed robbery that occurred in a room inside the Palace Station casino-hotel on Thursday.