Boselli has spent much of the last two seasons on loan after enduring a torrid time since arriving at the DW Stadium in 2010.
The Argentine striker returned to England this summer and scored the opening goal against Nottingham Forest in the Capital One Cup on Tuesday, much to the delight of Martinez.
The Wigan boss said: "We are very, very exited about Mauro, what we saw against Forest he's been doing all pre-season. His movement in the box is of someone very special in front of goal.
"I think he's happier now than he's ever been in the previous pre-seasons. I see him now with a bit of light in his eyes.
"He's desperate to work hard for the team and have an opportunity in the league. Nights like that help him towards achieving that."
Wigan are looking for three successive wins in all competitions when they take on Stoke City on Saturday, September 1.