Bale is expected to be confirmed as a Spurs player again soon having struggled in recent times at Real Madrid.
His arrival back in north London is expected to put Tottenham back in contention for the Premier League top four.
But Arteta, who is manager at Tottenham’s north London rivals Arsenal, is looking at the positives of the Welshman’s return.
Arteta said: “The Premier League in its history has always had the best players in the world.
“I think Gareth has been one of the most significant names that left the Premier League years ago to go to Spain, so I think it's really positive to bring really important players back to the league and it will be a challenge because we know at his best what he can do.
"I think the competition from every club, the way they are all recruiting and improving their squad, is making this league harder and harder."
Tottenham are looking to get back into the Prem top four while Liverpool are hoping to keep hold of their maiden title.
The Reds signed Thiago from Bayern Munich on Friday but Arsenal legend Ray Parlour believes Bale to Spurs is a better signing.
“I think Bale can bring more to the team for Tottenham,” Parlour told talkSPORT.
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“I think Liverpool are an excellent team anyway and that strengthens the midfield; they’ve got Henderson, Wijnaldum, Oxlade-Chamberlain.
“They’ve got so many good players in there, but Thiago is an excellent signing.
“But I think if you can get the best out of Bale and get him fit, I think Bale will be a better signing.”