Mohamed Elneny could make his Arsenal debut against Stoke on Sunday
The 23-year-old midfielder had been forced to stay in Paris, France, as he awaited clearance on his visa.
But his arrival today means the Egyptian international is able to finalise the £7.4m move from Basel.
Speaking on Monday, Wenger was hopeful the deal would be concluded this week.
"I expect movement this week,” Wenger said.
"We are positive this week that it can happen.
"The situation should be sorted out this week as there are a lot of work permit problems as well and special paperwork to do such as his visa."
Elneny is expected to sign a four-and-a-half year deal and could be in the frame to make his debut against Stoke on Sunday afternoon.
He will provide much needed strength in depth for Arsenal in midfield after a number of injuries in that position.
Francis Coquelin and Santi Cazorla are not expected back until the end of February after both suffered knee injuries.
Jack Wilshere has been out since the start of the season with a hairline fracture and his attempts to resume full training have been postponed.
But Wenger still retains confidence that the England ace will return and realise his potential.
Wenger said: "I am an optimist.
"I always think: 'Okay, it's true that he hasn't played many games in recent years'.
"I hope at some stage that will stop because he is young and I hope I'm right.
"He is a special case because he is a special talent and he comes out of the club. And he is an England international and I hope his injuries will stop at some stage."