The pair sealed late moves which took place just before the transfer window closed, with Kightly heading to Burnley and Shotton joining Wigan.
The winger will spend the season at Turf Moor, where he will work with manager Sean Dyche, under whom he played during a loan spell at Watford in 2011. The defender, meanwhile, heads to the Latics, who endured a busy deadline day, also bringing in Nick Powell while James McCarthy left for Everton.
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"It's been a whirlwind evening and we only found out really late about Wigan’s interest. I can't wait to get going now and meet the players," Shotton told the club's official website.
"As soon as I spoke to the gaffer and he told me how much he wanted me, I made up my mind and now I can't wait to get started. The club is obviously moving forwards and the squad here is really impressive. The competition for places is intense but that is what all players need and I'm going to do everything I can to win a place in the team.
"I played a big part in the European campaign for Stoke and that's something else that's really appealing about the club.
"I just want to say a big thanks to everyone at Stoke City. It's a club I've been at for 16 years so it's played a huge part of my life. Who knows what will happen in the future but for now I'm a Wigan player and I can't wait to get started."