The Championship side announced a verbal agreement was in place yesterday but today confirmed the deal had been completed.
Martinez, 22, has made eight appearances for the Gunners and will make his debut in tonight's Capital One Cup tie.
"We are delighted to have brought Emi to the club for the season," said head coach Kenny Jackett.
"It is very important to have good competition among your goalkeepers, not just at the start of the season but as it progresses.
"So it is good to bring Emi in right at the start and we are looking forward to working with him."
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