The versatile 31-year-old, who was a free agent after leaving Norwich, joined the Championship table-toppers after impressing during a successful loan spell with the club at the end of 2012.
And Turner is looking forward to working with Lappin again.
"The fans won't have seen too much of him yet but he's a very good left-back in my opinion," Turner told the club's official website.
"I played with him in one game at Birmingham and I've trained with him a lot - he's a very accomplished footballer.
"He's tidy on the ball, can defend and hits a good ball and I think he's exactly the sort of player we're looking for as we were probably short numbers in terms of the back four.
"He ticks that box, but he's also a very good player, so I'm looking forward to working with him further."
City travel to Huddersfield on Saturday with a 10-point cushion at the top of the table.