The North London outfit sealed the Chile international's signature from Barcelona yesterday for a fee believed to be in the region of £30m.
While Barton believes that the 25-year-old's arrival will boost the Gunners next season, the former Newcastle United midfielder is unsure if the "inconsistent" forward will push Arsenal back to dominating ways.
The 31-year-old wrote on Twitter: "Am I the only one not overly wetting my pants over Arsenal signing Sanchez? From what I've seen of him he is incredibly inconsistent.
"Yes, on his day he can light up a game. But as anyone who has watched Barca will tell you. His good games are as common as his bad.
"Whilst I think it will improve Arsenal. They still need more if they are to challenge for the title. Still think they need a bit of steel. He plays better for Chile where he's the main man than Barca where he's in Messi's shadow. Will he be the main man at the Emirates?"
Liverpool were also linked with a move for the forward as part of a deal which is expected to take Luis Suarez to the Camp Nou, but widespread reports have claimed that Sanchez was not keen on a switch to Merseyside.