The 28-year-old Maloney travelled to Lancashire earlier in the day after the two clubs agreed a fee, believed to be about £1 million.
Maloney's deal includes the option for an additional third year.
"We're delighted to welcome Shaun, who has great experience and is at the perfect age to come and bring something different to our squad," said manager Roberto Martinez.
Maloney said: "I spoke to the manager a couple of days ago and that started to be the reason why, over the last couple of days, I thought this would be something that excites me. I can't wait to get started."
He added: "After speaking with both clubs, I decided it was probably the right time - especially the league Wigan are in, it is just something that straight away appealed.
"And the manager was that positive when I spoke to him that you just want to come and train and play under him."
"Patrick is a player with enormous potential," Martinez said. "Technically he is very gifted, very comfortable in possession and physically, he uses his intensity to defend very effectively.
"He can play left back or left wing back position and without a doubt he's got a phenomenal career ahead of him and I hope he can settle in Wigan really quickly and start enjoying his football as a Latics player."